user-1: I posted the identikit question to Christianity stackexchange, and was met with dumb silence.
Which, really, I was shocked by. E.g. the parable of the good samaratin:

Jesus answered, "A certain man was going down from Jerusalem to
Jericho, and he fell among robbers, who both stripped him and beat
him, and departed, leaving him half dead. By chance a certain priest
was going down that way. When he saw him, he passed by on the other
side. In the same way a Levite also, when he came to the place, and
saw him, passed by on the other side. But a certain Samaritan, as he
travelled, came where he was. When he saw him, he was moved with
compassion, came to him, and bound up his wounds, pouring on oil and
wine. He set him on his own animal, and brought him to an inn, and
took care of him. On the next day, when he departed, he took out two
denarii, and gave them to the host, and said to him, 'Take care of
him. Whatever you spend beyond that, I will repay you when I return.'
Now which of these three do you think seemed to be a neighbour to him
who fell among the robbers?"
He said, "He who showed mercy on him."
Then Jesus said to him, "Go and do likewise."

'Mercy' can be defined as

compassion or forgiveness shown towards someone whom it is within
one's power to punish or harm.

Which is very, very close to exactly what I mean: compassion towards someone who you have punished or harmed.
Because it seems to me to be the bedrock of intelligent ethics, I was very interested in if the Buddha ever discussed this.

Did the Buddha ever teach that we have a special responsibility to
those we have injured?


user-1: Yes householder, interested,
Reconciliation is very important to be able to move on, so one should, when ever there is a change, seek after such.

"Monks, these two are fools. Which two? The one who doesn't see his transgression as a transgression, and the one who doesn't rightfully pardon another who has confessed his transgression. These two are fools. Bala-pandita Sutta: Fools & Wise People

As it is not always possible, there are placed less duties, but there have been given such for Bhikkhus, especially toward lay people and such is also needed in cases where the monks have rightly turned over the bowl for lay people. And there are also transactions within the community.
In the first case, having done wrong toward a lay person, there is even a detail way how to do it and that such as reconciliation is very needed within relations.
There is a generous work by Bhante Thanissaro on this matter: Reconciliation, Right & Wrong
One may let it be known if details are wished to get known to understand this matter well for a possibility to walk on, since not done blocks one 100% off.
Being that important, follower would ask the teacher and Tripple Gems on each meeting anew for forgiveness (Vandami) since otherwise the "first precept" is broken and no change to ever success in Dhamma. As known wrongdoing toward them can be a matter that leads to hell and cuts one off totally.

Requesting Forgiveness from the Tripple Gems:
Repeat Namo... three times. Then:
Ratanattaye pamādena, dvārattayena kataṃ,
Sabbaṃ aparādhaṃ khamatu no bhante.
May the Triple Gem forgive us for any wrong we have done out of carelessness in thought, word, or deed.

...from Monk(s), teacher...
Repeat Namo... three times. Then:
[Mahāthere]* pamādena, dvārattayena kataṃ,
Sabbaṃ aparādhaṃ khamatu no bhante.
(Three times.)
Venerable Sir, may you forgive us for any wrong >we have done you out of carelessness in thought, >word, or deed.
[* Mahāthere is used for very senior & >highly respected monks. Change it to There for >somewhat less senior monks, Upajjhāye for one's >preceptor, Ācariye for one's teacher, and >Āyasmante for monks in general.]
Bow down & stay there while the monk says:
Ahaṃ khamāmi, tumhehi pi me khamitabbaṃ.
I forgive you; may you all also forgive me.

Extended and usual forms found in the morning and evening recitations.
So especially parents, teacher, supporter, and Tripple Gems: hurry up if there is anything not solved!
(Note that this is not given for trade, exchange, stacks, entertainment and akusala deeds, but as a share of merits and continue such for release)

user8157: Yes. Buddhism teaches if we have performed a harmful action and we become conscientiously aware we harmed, we should ask for forgiveness and do whatever we can do to reconcile the matter.
For example, the scriptures contain the following stock phrase:

But because you see your transgression as such and make amends in
accordance with the Dhamma, we accept your confession. For it is a
cause of growth in the Dhamma & Discipline of the noble ones when,
seeing a transgression as such, one makes amends in accordance with
the Dhamma and exercises restraint in the future.

The scriptures also contain the following teaching:

These two are wise people. Which two? The one who sees his transgression as a transgression, and the one who rightfully pardons another who has confessed his transgression. These two are wise people.
Monks, these two are fools. Which two? The one who doesn't see his transgression as a transgression, and the one who doesn't rightfully pardon another who has confessed his transgression. These two are fools.

It follows the robbers in the Parable of the Good Samaritan have no special responsibility in Buddhism because they were not conscientiously aware and they were not Buddhists. The Buddhist Path is only for Buddhists.
For example, puthujjana ('blind worldlings') often attempt to harm my efforts to teach to the True Dhamma but I have no expectations towards them to have 'mercy' on me because they are puthujjana ('blind worldlings'). Their destination of "hell" is already determined by their actions. Jesus said: "Forgiven them Father, for they know not what they do". Similarly, the Buddha taught all unskillful actions have ignorance or not-knowing as their source.

The Blessed One said, "Monks, ignorance is the leader in the attainment of unskillful qualities, followed by lack of conscience &
lack of concern.
Avijja Sutta

Since the ignorant do not know what they are doing is wrong & harmful, it is not possible they have a sense of special responsibility. They will continue to act motivated by what they believe is 'right', even though they are wrong & harm themselves, others & even the Buddha-Dhamma.

user254: the parable of the good samaritan
The parable of the Good Samaritan isn't about "special responsibility to those we have injured". In the parable:

The "certain man" was injured by robbers (who stripped and beat him)
The injured man was ignored by a priest and a Levite
The Samaritan showed compassion and acted as if he had a special responsibility (even though the Samaritan had nothing to do with, wasn't responsible for, causing the man's injury)
Jesus's message is to do like the Samaritan did


'Mercy' can be defined as compassion or forgiveness shown towards someone whom it is within one's power to punish or harm.
You seem to be interested in the definition of "mercy".
I slightly disagree with your definition above. If you're able to rescue someone from drowning, for example, then that could an act of mercy, but (assuming you weren't the cause of their being in the water) nothing to do with "punishing" or "harming".
You might like Wikipedia's article on Mercy (I went to it to look for the etymology of the word). An interesting part is at the end,

To be mercy, the behavior generally can not be compelled by outside forces. A famous literary example that alludes to the impact of the ethical components of the mercy on the legal aspects is from The Merchant of Venice when Portia asks Shylock to show mercy. He asks, "On what compulsion, must I?" She responds:

The quality of mercy is not strain'd.
It droppeth as the gentle rain from heaven
Upon the place beneath. It is twice blest:
It blesseth him that gives and him that takes.


That almost argues against your definition: because there might be some special obligation towards someone you have injured.
The corresponding traditional Buddhist virtues, by the way, if you want to research them further, might be the Brahmaviharas (including Karuṇā which is 'translated' as compassion), and ahimsa (harmlessness or non-violence, for example mentioned here).

compassion towards someone who you have punished or harmed
There may be something somewhere in Buddhist scripture, that talks about whether and how to behave towards people you have injured.
Although that's your question I'm not immediately inclined to answer it, because the more important message of Buddhism is, "because you have compassion for people, do not cause them injury".
The basic rules of conduct, for example the five precepts, and the ethical conduct portion of the eight-fold way, are to do with not causing injury.
One of the suttas about the five precepts starts with,

There are these five gifts, five great gifts — original, long-standing, traditional, ancient, unadulterated, unadulterated from the beginning — that are not open to suspicion, will never be open to suspicion, and are unfaulted by knowledgeable contemplatives & brahmans. Which five?
There is the case where a disciple of the noble ones, abandoning the taking of life, abstains from taking life. In doing so, he gives freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings. In giving freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings, he gains a share in limitless freedom from danger, freedom from animosity, and freedom from oppression. This is the first gift, the first great gift — original, long-standing, traditional, ancient, unadulterated, unadulterated from the beginning — that is not open to suspicion, will never be open to suspicion, and is unfaulted by knowledgeable contemplatives & brahmans...

The practice of Dana (i.e. gift-giving or generosity) is made especially by laypeople towards monks and nuns; and not because those monks and nuns were injured by the laypeople.

Because it seems to me to be the bedrock of intelligent ethics
Some people think that the "golden rule" is the bedrock of intelligent ethics, e.g. "do unto others as you would have others do unto you", also known as "love thy neighbour as thyself".
I think you'll find that in Buddhism too, for example in the Dhammapada,


All tremble at violence; all fear death. Putting oneself in the place of another, one should not kill nor cause another to kill.

All tremble at violence; life is dear to all. Putting oneself in the place of another, one should not kill nor cause another to kill.

One who, while himself seeking happiness, oppresses with violence other beings who also desire happiness, will not attain happiness
hereafter.

One who, while himself seeking happiness, does not oppress with violence other beings who also desire happiness, will find happiness
hereafter.

Speak not harshly to anyone, for those thus spoken to might retort. Indeed, angry speech hurts, and retaliation may overtake you.




Did the Buddha ever teach that we have a special responsibility to those we have injured?
I'm pretty sure he taught that we have some responsibility to not injure people.
I think that the practice of deliberately (intentionally) injuring someone would be likely to have a negative/undesirable karmic consequence.
I'm not sure it's always possible to undo an injury (which is a reason for avoiding causing injury in the first place).
Answers to other topics on this site, for example What do we do when we've broken a precept?, don't seem to focus on restitution or special responsibility towards the injured party.
The practice of the Buddhist "Metta Bhavana" (or "cultivation of loving-kindness") meditation is meant to develop compassion towards all people, both near and far, both more dear and less dear -- and not especially towards "someone you have punished or injured".

-1: <p>I posted the identikit question to Christianity stackexchange, and was met with dumb silence.</p>
<p>Which, really, I was shocked by. E.g. the parable of the good samaratin:</p>
<blockquote>
<p>Jesus answered, &quot;A certain man was going down from Jerusalem to
Jericho, and he fell among robbers, who both stripped him and beat
him, and departed, leaving him half dead. By chance a certain priest
was going down that way. When he saw him, he passed by on the other
side. In the same way a Levite also, when he came to the place, and
saw him, passed by on the other side. But a certain Samaritan, as he
travelled, came where he was. When he saw him, he was moved with
compassion, came to him, and bound up his wounds, pouring on oil and
wine. He set him on his own animal, and brought him to an inn, and
took care of him. On the next day, when he departed, he took out two
denarii, and gave them to the host, and said to him, 'Take care of
him. Whatever you spend beyond that, I will repay you when I return.'
Now which of these three do you think seemed to be a neighbour to him
who fell among the robbers?&quot;</p>
<p>He said, &quot;He who showed mercy on him.&quot;</p>
<p>Then Jesus said to him, &quot;Go and do likewise.&quot;</p>
</blockquote>
<p>'Mercy' can be defined as</p>
<ul>
<li>compassion or forgiveness shown towards someone whom it is within
one's power to punish or harm.</li>
</ul>
<p>Which is very, very close to exactly what I mean: compassion towards someone who you have punished or harmed.</p>
<p>Because it seems to me to be <em>the bedrock</em> of intelligent ethics, I was very interested in if the Buddha ever discussed this.</p>
<ol>
<li>Did the Buddha ever teach that we have a special responsibility to
those we have injured?</li>
</ol>
 -1: <p>Yes householder, interested,</p>
<p>Reconciliation is very important to be able to move on, so one should, when ever there is a change, seek after such.</p>
<blockquote>
<p>&quot;Monks, these two are fools. Which two? The one who doesn't see his transgression as a transgression, and the one who doesn't rightfully pardon another who has confessed his transgression. These two are fools. <a href="http://zugangzureinsicht.org/html/tipitaka/an/an02/an02.021.than_en.html" rel="nofollow noreferrer">Bala-pandita Sutta: Fools &amp; Wise People</a></p>
</blockquote>
<p>As it is not always possible, there are placed less duties, but there have been given such for Bhikkhus, especially toward lay people and such is also needed in cases where the monks have rightly turned over the bowl for lay people. And there are also transactions within the community.</p>
<p>In the first case, having done wrong toward a lay person, there is even a detail way how to do it and that such as reconciliation is very needed within relations.</p>
<p>There is a generous work by Bhante Thanissaro on this matter: <a href="http://zugangzureinsicht.org/html/lib/authors/thanissaro/reconciliation_en.html" rel="nofollow noreferrer">Reconciliation, Right &amp; Wrong</a></p>
<p>One may <a href="http://zugangzureinsicht.org/html/lib/authors/wijesinghe/punna_en.html" rel="nofollow noreferrer">let it be known</a> if details are wished to get known to understand this matter well for a possibility to walk on, since not done blocks one 100% off.</p>
<p>Being that important, follower would ask the teacher and Tripple Gems on each meeting anew for forgiveness (<a href="http://zugangzureinsicht.org/html/lib/authors/dhammayut/chanting_en.html#forgiveness" rel="nofollow noreferrer">Vandami</a>) since otherwise the &quot;first precept&quot; is broken and no change to ever success in Dhamma. As known wrongdoing toward them can be a matter that leads to hell and cuts one off totally.</p>
<blockquote>
<p><strong>Requesting Forgiveness</strong> from the Tripple Gems:</p>
<p>Repeat Namo... three times. Then:</p>
<p><em>Ratanattaye pamādena, dvārattayena kataṃ,</em>
<em>Sabbaṃ aparādhaṃ khamatu no bhante.</em></p>
<p>May the Triple Gem forgive us for any wrong we have done out of carelessness in thought, word, or deed.</p>
<hr />
<p>...from Monk(s), teacher...</p>
<p>Repeat Namo... three times. Then:</p>
<p>[Mahāthere]* <em>pamādena, dvārattayena kataṃ,</em>
<em>Sabbaṃ aparādhaṃ khamatu no bhante.</em>
(Three times.)</p>
<p>Venerable Sir, may you forgive us for any wrong &gt;we have done you out of carelessness in thought, &gt;word, or deed.</p>
<p>[* Mahāthere is used for very senior &amp; &gt;highly respected monks. Change it to There for &gt;somewhat less senior monks, Upajjhāye for one's &gt;preceptor, Ācariye for one's teacher, and &gt;Āyasmante for monks in general.]</p>
<p>Bow down &amp; stay there while the monk says:</p>
<p><em>Ahaṃ khamāmi, tumhehi pi me khamitabbaṃ.</em></p>
<p>I forgive you; may you all also forgive me.</p>
</blockquote>
<p>Extended and usual forms found in the <a href="http://zugangzureinsicht.org/html/lib/authors/dhammayut/chanting_en.html" rel="nofollow noreferrer">morning and evening recitations</a>.</p>
<p>So especially parents, teacher, supporter, and Tripple Gems: hurry up if there is anything not solved!</p>
<p><em>(Note that this is not given for trade, exchange, stacks, entertainment and akusala deeds, but as a share of merits and continue such for release)</em></p>
 8157: <p>Yes. Buddhism teaches if we have performed a harmful action and we become <em>conscientiously</em> <em>aware</em> we harmed, we should ask for forgiveness and do whatever we can do to reconcile the matter.</p>
<p>For example, the scriptures contain the following stock phrase:</p>
<blockquote>
<p><em>But because you see your transgression as such and make amends in
accordance with the Dhamma, we accept your confession. For it is a
cause of growth in the Dhamma &amp; Discipline of the noble ones when,
seeing a transgression as such, one makes amends in accordance with
the Dhamma and exercises restraint in the future.</em></p>
</blockquote>
<p>The scriptures also contain the following teaching:</p>
<blockquote>
<p><em>These two are wise people. Which two? The one who sees his transgression as a transgression, and the one who rightfully pardons another who has confessed his transgression. These two are wise people.</em></p>
<p><em>Monks, these two are fools. Which two? The one who doesn't see his transgression as a transgression, and the one who doesn't rightfully pardon another who has confessed his transgression. These two are fools.</em></p>
</blockquote>
<p>It follows the robbers in the Parable of the Good Samaritan have no special responsibility in Buddhism because they were not <em>conscientiously</em> <em>aware</em> and they were not Buddhists. The Buddhist Path is only for Buddhists.</p>
<p>For example, <em>puthujjana</em> ('<em>blind worldlings</em>') often attempt to harm my efforts to teach to the True Dhamma but I have no expectations towards them to have 'mercy' on me because they are <em>puthujjana</em> ('<em>blind worldlings</em>'). Their destination of &quot;<a href="https://www.accesstoinsight.org/tipitaka/mn/mn.130.than.html" rel="nofollow noreferrer">hell</a>&quot; is already determined by their actions. Jesus said: &quot;<em>Forgiven them Father, for they know not what they do</em>&quot;. Similarly, the Buddha taught all unskillful actions have ignorance or not-knowing as their source.</p>
<blockquote>
<p><em>The Blessed One said, &quot;Monks, ignorance is the leader in the attainment of unskillful qualities, followed by lack of conscience &amp;
lack of concern.</em></p>
<p><em>Avijja Sutta</em></p>
</blockquote>
<p>Since the ignorant do not know what they are doing is wrong &amp; harmful, it is not possible they have a sense of special responsibility. They will continue to act motivated by what they believe is 'right', even though they are wrong &amp; harm themselves, others &amp; even the Buddha-Dhamma.</p>
 254: <p><strong>the parable of the good samaritan</strong></p>
<p>The parable of the Good Samaritan <em>isn't</em> about &quot;special responsibility to those we have injured&quot;. In the parable:</p>
<ul>
<li>The &quot;certain man&quot; was injured by robbers (who stripped and beat him)</li>
<li>The injured man was ignored by a priest and a Levite</li>
<li>The Samaritan showed compassion and acted as if he had a special responsibility (even though the Samaritan had nothing to do with, wasn't responsible for, causing the man's injury)</li>
<li>Jesus's message is to do like the Samaritan did</li>
</ul>
<hr />
<p><strong>'Mercy' can be defined as compassion or forgiveness shown towards someone whom it is within one's power to punish or harm.</strong></p>
<p>You seem to be interested in the definition of &quot;mercy&quot;.</p>
<p>I slightly disagree with your definition above. If you're able to rescue someone from drowning, for example, then that could an act of mercy, but (assuming you weren't the cause of their being in the water) nothing to do with &quot;punishing&quot; or &quot;harming&quot;.</p>
<p>You might like Wikipedia's article on <a href="https://en.wikipedia.org/wiki/Mercy" rel="nofollow noreferrer">Mercy</a> (I went to it to look for the etymology of the word). An interesting part is at the end,</p>
<blockquote>
<p>To be mercy, the behavior generally can not be compelled by outside forces. A famous literary example that alludes to the impact of the ethical components of the mercy on the legal aspects is from The Merchant of Venice when Portia asks Shylock to show mercy. He asks, &quot;On what compulsion, must I?&quot; She responds:</p>
<blockquote>
<p>The quality of mercy is not strain'd.<br />
It droppeth as the gentle rain from heaven<br />
Upon the place beneath. It is twice blest:<br />
It blesseth him that gives and him that takes.</p>
</blockquote>
</blockquote>
<p>That almost argues against your definition: because there might be some special obligation towards someone you have injured.</p>
<p>The corresponding traditional Buddhist virtues, by the way, if you want to research them further, might be <a href="https://en.wikipedia.org/wiki/Brahmavihara" rel="nofollow noreferrer">the Brahmaviharas</a> (including <a href="https://en.wikipedia.org/wiki/Karu%E1%B9%87%C4%81" rel="nofollow noreferrer">Karuṇā</a> which is 'translated' as compassion), and <em>ahimsa</em> (harmlessness or non-violence, <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.008.nypo.html" rel="nofollow noreferrer">for example mentioned here</a>).</p>
<hr />
<p><strong>compassion towards someone who you have punished or harmed</strong></p>
<p>There may be something somewhere in Buddhist scripture, that talks about whether and how to behave towards people you have injured.</p>
<p>Although that's your question I'm not immediately inclined to answer it, because the more important message of Buddhism is, &quot;because you have compassion for people, do not cause them injury&quot;.</p>
<p>The basic rules of conduct, for example the <a href="https://en.wikipedia.org/wiki/Five_Precepts" rel="nofollow noreferrer">five precepts</a>, and the <a href="https://en.wikipedia.org/wiki/Noble_Eightfold_Path#Ethical_conduct" rel="nofollow noreferrer">ethical conduct</a> portion of the eight-fold way, are to do with not causing injury.</p>
<p>One of the suttas about <a href="http://www.accesstoinsight.org/ptf/dhamma/sila/pancasila.html" rel="nofollow noreferrer">the five precepts</a> starts with,</p>
<blockquote>
<p>There are these five gifts, five great gifts — original, long-standing, traditional, ancient, unadulterated, unadulterated from the beginning — that are not open to suspicion, will never be open to suspicion, and are unfaulted by knowledgeable contemplatives &amp; brahmans. Which five?</p>
<p>There is the case where a disciple of the noble ones, abandoning the taking of life, abstains from taking life. <strong>In doing so, he gives freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings.</strong> In giving freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings, he gains a share in limitless freedom from danger, freedom from animosity, and freedom from oppression. This is the first gift, the first great gift — original, long-standing, traditional, ancient, unadulterated, unadulterated from the beginning — that is not open to suspicion, will never be open to suspicion, and is unfaulted by knowledgeable contemplatives &amp; brahmans...</p>
</blockquote>
<p>The <a href="http://www.accesstoinsight.org/lib/authors/various/wheel367.html" rel="nofollow noreferrer">practice of Dana</a> (i.e. gift-giving or generosity) is made especially by laypeople towards monks and nuns; and not because those monks and nuns were injured by the laypeople.</p>
<hr />
<p><strong>Because it seems to me to be the bedrock of intelligent ethics</strong></p>
<p>Some people think that the &quot;<a href="https://en.wikipedia.org/wiki/Golden_Rule" rel="nofollow noreferrer">golden rule</a>&quot; is the bedrock of intelligent ethics, e.g. &quot;do unto others as you would have others do unto you&quot;, also known as &quot;love thy neighbour as thyself&quot;.</p>
<p>I think you'll find that in Buddhism too, for example <a href="http://www.accesstoinsight.org/tipitaka/kn/dhp/dhp.10.budd.html" rel="nofollow noreferrer">in the Dhammapada</a>,</p>
<blockquote>
<ol start="129">
<li><p>All tremble at violence; all fear death. Putting oneself in the place of another, one should not kill nor cause another to kill.</p>
</li>
<li><p>All tremble at violence; life is dear to all. Putting oneself in the place of another, one should not kill nor cause another to kill.</p>
</li>
<li><p>One who, while himself seeking happiness, oppresses with violence other beings who also desire happiness, will not attain happiness
hereafter.</p>
</li>
<li><p>One who, while himself seeking happiness, does not oppress with violence other beings who also desire happiness, will find happiness
hereafter.</p>
</li>
<li><p>Speak not harshly to anyone, for those thus spoken to might retort. Indeed, angry speech hurts, and retaliation may overtake you.</p>
</li>
</ol>
</blockquote>
<hr />
<p><strong>Did the Buddha ever teach that we have a special responsibility to those we have injured?</strong></p>
<p>I'm pretty sure he taught that we have some responsibility to not injure people.</p>
<p>I think that the practice of deliberately (intentionally) injuring someone would be likely to have a negative/undesirable karmic consequence.</p>
<p>I'm not sure it's always possible to undo an injury (which is a reason for avoiding causing injury in the first place).</p>
<p>Answers to other topics on this site, for example <a href="https://buddhism.stackexchange.com/q/7555/254">What do we do when we've broken a precept?</a>, don't seem to focus on restitution or special responsibility towards the injured party.</p>
<p>The practice of the Buddhist &quot;Metta Bhavana&quot; (or &quot;cultivation of loving-kindness&quot;) meditation is meant to develop compassion towards all people, both near and far, both more dear and less dear -- and not especially towards &quot;someone you have punished or injured&quot;.</p>
