My student in one course asks for paid tutoring in another course. Appropriate? I'm a teaching assistant for an introductory programming course. A student in the course approached me and asked if I would tutor them for a different discrete mathematics course in return for payment. 

I grade all of the material for the programming course, and so I feel like there's a conflict of interest in receiving any payment from the student, even if its unrelated to the programming course.

Am I overthinking it or is it right to think there's an issue here?
You're correct in feeling uneasy.

Even if you are not yourself improperly influenced, there would definitely be the appearance of possibility of improper influence, which is as important, in terms of the impact on other peoples' actions, as actual impropriety.

Even tutoring _for_free_, since you are in the same dept as the people giving the other course, could be perceived as improper, for various reasons.

Best to keep "squeaky clean", I think.