What do you do if a person in your group purposely misleads you? I'm an undergraduate researcher working with another undergraduate researcher in a group. I believe the other undergraduate researcher wants to look particularly good between the two of us for a good letter of recommendation, and she has been doing this to my detriment (giving me false or misleading information on our shared project).

The graduate student that's also working on the project now certainly prefers her and sees me as kind of useless. Of course, I'm going to try to just perform well independently now to see if I can demonstrate my value, but I'm wondering if this sort of a thing is appropriate to bring up, and if so how. I'm only here for a Summer.

Edit:
As an update for whoever is interested, I found a solution. The other students' only incentive is to look good, though thus far it has been to my detriment. I asked the other student openly if they thought I unfairly got the short end of the stick in our last meeting, and she agreed that I did. So then we agreed that if she actively made clear the work that I was doing in the next meeting, that I would do the same for her. This way all our efforts are acknowledged, so there's no need to employ subterfuge, and so there's no drama involved. The grad student acknowledges both our efforts now. A game-theoretic perspective can be helpful sometimes! I'm happy I can proceed together with the other student on our project.
Unfortunately it happens, not just in undergraduate research. 

What you should or could do strongly depends on your evidence and the perceptions of other people involved, here supervisors. However, assume you are right and you have evidence, still then supervisors often do not like to hear you complaining about someone they like or value. You will not change their minds easily.

So my advise would be to follow what you expressed already. Just perform well independently. But also make sure that your work and effort is visible. You may need to step out of your comfort zone and be more extrovert and assertive. If you do not occupy your space, others will. 

You can see this as an excellent learning opportunity to improve these skills. Try to park the negative emotion for now if it does not help. Do not deny it but promise yourself to assess it later. Experiment with different behaviour and approaches and consider it as a training in personal leadership. After the summer make a list with behaviour you considered effective and less effective. 

Wish you all the best.