Someone reported cheating during a quiz, but I didn't catch it myself

You're the teaching assistant. Inform the professor and let them handle the matter or offer you guidance. That's their job. In this case the evidence for cheating is tenuous at best, so I suspect nothing will be done against any of the students. I've known more compelling cases of cheating to go reasonably unpunished, and one case of very blatant (and easily proved) cheating that was handled with just a stern admonishment and warning from the professor. But you (and the professor) would rather the professor hear of the matter through you, than the possibly salacious gossip of the students.

So what what really needs to be addressed is:

Always keep your eye on the students during exams/quizzes.

As much as you want to believe that they're all perfectly moral and self-policing people (and quite probably most of them are), or that they can't possibly fit in cheating during "brief" windows, there will always be exceptions, and you owe it to the students who are such from giving such a clear opening to those who aren't (for whatever reasons). You can't prevent all cheating all the time—it comes in a lot of forms, and some people are really good at it—, but this was easily preventable.

You may find yourself needing to apologize to the professor for this lapse, though I wouldn't get too worked up over that. Most of us have made such a mistake at some point (although not all of us may be aware of it), and the minor value of the quiz helps take the edge off, such that a simple apology and recognition of the error is sufficient to make things right.

Perhaps my opinion is less valid given I have only tutored groups of students, and have not yet had formal teaching experience. But, again, perhaps a recent undergrad student opinion would be helpful. In my opinion, you can not reprimand students for cheating without witnessing it yourself, or having a very good reason (backed up by solid evidence) to penalize them for cheating.

Obviously, it seems likely this student that called them out was probably not lying, unless she's a sociopath. So, they either were using notes, or this other student saw what she thought were notes, but actually weren't. Either way, you can not really punish the students without further evidence. Academic dishonesty is a serious accusation that can tarnish a student's reputation for the entirety of their academic career. Evidence is a must. However, I don't think it would be a problem if you just point-blank asked them if they were using notes and deliberately cheating.