user-1: Have any important Buddhists made any claim/s about Krishnamurti's teachings? Especially (caveat I know nothing about this) his claim that 

"Tell them there is nothing to understand"

Bold emphasis is mine.
or

He claimed that the demand for enlightenment was the only thing
  standing in the way of enlightenment itself, if enlightenment existed
  at all.


user738: I have not found anything about "Buddhists" saying anything about UG Krishnamurti. UG Krishnamurti was too low key anyway to take a "religion" seriously and for any "eminent Buddhists" to think about him. Perhaps the "Buddhists" here can offer some opinion(of course that would just make the site go on).
There's one thing I'd like to add here. UG Krishnamurti will not come off as a gentle man when he speaks and he speaks very controversially about other religions and religious leaders. People may not like it but he didn't care about it either. 

user10304: I only just read the title, and try to answer. 

Have any notable Buddhists commented on Krishnamurti's teachings?

I think Jiddu Krishnamurti (not U. G.) is not particularly being concerned by any Buddhist. If you don't ask this question, this is not really a dish that's waiting to be served. This dish may even not exist.   
From past material I read, he was "chosen" by the Theosophical Society and groomed to be a spiritual leader, later he rebelled. Theosophical Society one of the founders was Helena Blavatsky who had learnt something from the Tibetan Lama, thus formulated her theory about the 5/7(?) races, the Atlanteans, Lemurians... and the Aryans are the supreme race... her theory later was adopted by Hitler... then we will have to go on analyzing the hands playing in the dark under the table, the world history and wars how these happened... OK. Pause. 
According to @sandeepani:
The Theosophical Society has helped the reviving of Buddhism greatly during the British Colonial Era in Sri Lanka and elsewhere. But their teachings were somewhat different still (a lot of mythical interest and combining religions), which caused many Buddhist members to leave it in later years.
If you are seeking to nourish your spirit, your inner life, my advice is to seek pure, pristine teachings from great teachers.  

user7138: I have read a remark by Ajahn Sumedho on Krishnamurti. I don't recall much of the details. But I can tell you that Krishnamurti 's teachings are different from Buddhism, although he has practiced Vipassana himself.
Edit: My answer relates to Jiddu Krishnamurthi, not U. G. Krishnamurthi. I am unfamiliar with U.G.

Sometimes you hear monks or nuns or lay people here saying, 'Don't attach to anything.' So we attach to the view that we shouldn't be attached! 'I'm not going to attach to Ajahn Sumedho; I can learn from anybody. I'm going to leave, just to prove I'm not attached to Venerable Sumedho.' Then you're attaching to the idea that you shouldn't be attached to me, or that you've got to go away to prove that you're not attached – which isn't it at all. That's not being wise, is it? You're just attaching to something else. You may go to Brockwood Park and hear Krishnamurti' and then you think – 'I'm not going to attach to those religious conventions, all that bowing, Buddha images, monks and all that stuff. Krishnamurti says it is all poppycock: "Don't have anything to do with it, all that is useless." ' So you attach to the view that religious conventions are all useless, and you shouldn't have anything to do with them. But that's also an attachment, isn't it? – attachment to views and opinions – and if you attach to what Krishnamurti says, or you attach to what I say, it's still an attachment.
Ajahn Sumedho
You can be attached to the idea of not being attached. Krishnamurti, for example, would always emphasise not to be attached to anything. He would say, 'Monks, this is all wrong. Religion, monks, all this is wrong. It's not the way.' Then people listening to that would attach to his view, and they weren't aware of the attachment they had to Krishnamurti's view. So the problem is not the view, but the attachment. A view is a view. You can see if you're attached to a view, for or against it. Then the actual practice is to not being attached to any view, and you are very much investigating what's going on.
Ajahn Sumedho

Edit: I added a separate answer on U. G. Krishnamurthi.

-1: <p>Have any important Buddhists made any claim/s about <a href="https://en.wikipedia.org/wiki/U._G._Krishnamurti" rel="nofollow noreferrer">Krishnamurti's</a> teachings? Especially (caveat I know nothing about this) his claim that </p>

<blockquote>
  <p>"Tell them <strong>there is <em>nothing</em> to understand</strong>"</p>
</blockquote>

<p>Bold emphasis is <a href="https://en.wikipedia.org/wiki/U._G._Krishnamurti" rel="nofollow noreferrer">mine</a>.</p>

<p>or</p>

<blockquote>
  <p>He claimed that the demand for enlightenment was the only thing
  standing in the way of enlightenment itself, if enlightenment existed
  at all.</p>
</blockquote>
 738: <p>I have not found anything about "Buddhists" saying anything about UG Krishnamurti. UG Krishnamurti was too low key anyway to take a "religion" seriously and for any "eminent Buddhists" to think about him. Perhaps the "Buddhists" here can offer some opinion(of course that would just make the site go on).</p>

<p>There's one thing I'd like to add here. UG Krishnamurti will not come off as a gentle man when he speaks and he speaks very controversially about other religions and religious leaders. People may not like it but he didn't care about it either. </p>
 10304: <p>I only just read the title, and try to answer. </p>

<blockquote>
  <p>Have any notable Buddhists commented on Krishnamurti's teachings?</p>
</blockquote>

<p>I think Jiddu Krishnamurti <em>(not U. G.)</em> is not particularly being concerned by any Buddhist. If you don't ask this question, this is not really a dish that's waiting to be served. This dish may even not exist.   </p>

<p>From past material I read, he was "chosen" by the Theosophical Society and groomed to be a spiritual leader, later he rebelled. Theosophical Society one of the founders was Helena Blavatsky who had learnt something from the Tibetan Lama, thus formulated her theory about the 5/7(?) races, the Atlanteans, Lemurians... and the Aryans are the supreme race... her theory later was adopted by Hitler... then we will have to go on analyzing the hands playing in the dark under the table, the world history and wars how these happened... OK. Pause. </p>

<p><em>According to @sandeepani:</em>
<em>The Theosophical Society has helped the <code>reviving</code> of Buddhism greatly during the British Colonial Era in Sri Lanka and elsewhere. But <strong>their teachings were somewhat different</strong> still (a lot of mythical interest and combining religions), which caused many Buddhist members to leave it in later years.</em></p>

<p>If you are seeking to nourish your spirit, your inner life, my advice is to seek pure, pristine teachings from great teachers.  </p>
 7138: <p>I have read a remark by Ajahn Sumedho on Krishnamurti. I don't recall much of the details. But I can tell you that Krishnamurti 's teachings are different from Buddhism, although he has practiced Vipassana himself.</p>
<p>Edit: My answer relates to Jiddu Krishnamurthi, not U. G. Krishnamurthi. I am unfamiliar with U.G.</p>
<blockquote>
<p><em>Sometimes you hear monks or nuns or lay people here saying, 'Don't attach to anything.' So we attach to the view that we shouldn't be attached! 'I'm not going to attach to Ajahn Sumedho; I can learn from anybody. I'm going to leave, just to prove I'm not attached to Venerable Sumedho.' Then you're attaching to the idea that you shouldn't be attached to me, or that you've got to go away to prove that you're not attached – which isn't it at all. That's not being wise, is it? You're just attaching to something else. You may go to Brockwood Park and hear Krishnamurti' and then you think – 'I'm not going to attach to those religious conventions, all that bowing, Buddha images, monks and all that stuff. Krishnamurti says it is all poppycock: &quot;Don't have anything to do with it, all that is useless.&quot; ' So you attach to the view that religious conventions are all useless, and you shouldn't have anything to do with them. But that's also an attachment, isn't it? – attachment to views and opinions – and if you attach to what Krishnamurti says, or you attach to what I say, it's still an attachment.</em></p>
<p><a href="http://www.dhammatalks.net/Books2/Ajahn_Sumedho_Cittaviveka.htm" rel="nofollow noreferrer">Ajahn Sumedho</a></p>
<p><em>You can be attached to the idea of not being attached. Krishnamurti, for example, would always emphasise not to be attached to anything. He would say, 'Monks, this is all wrong. Religion, monks, all this is wrong. It's not the way.' Then people listening to that would attach to his view, and they weren't aware of the attachment they had to Krishnamurti's view. So the problem is not the view, but the attachment. A view is a view. You can see if you're attached to a view, for or against it. Then the actual practice is to not being attached to any view, and you are very much investigating what's going on.</em></p>
<p><a href="http://www.dhammatalks.net/Books3/Ajahn_Sumedho_Question_Time.htm" rel="nofollow noreferrer">Ajahn Sumedho</a></p>
</blockquote>
<p>Edit: I added a separate answer on U. G. Krishnamurthi.</p>
