How should I deal with incorrect information given to me by a TA
Yes, tell the professor about it. You shouldn't make a huge deal out of it, but send a brief, neutral e-mail saying that you were given wrong information in the office hours, that you got the impression the student was distracted and not really listening to what you said, and maybe ask how you can ensure that you do not waste time on red herrings next time.

If it's a one-off, and the student just had a bad day or a pressing deadline, it shouldn't have a big impact, but if other students also report similar problems the prof may watch the TA's performance a bit more closely, and may even decide to hire a different TA next year.

End-of-semester evaluations are also a good place to note this kind of experience. In my university the TAs even get their own evaluation form.