We have a customer who is asking for a copy of a check they deposited into there account several months ago. Do you see a problem with us providing copies of previously deposited checks?

No

I sure hope not. We do it all the time.

I do think you should have a research or copy fee for such requests.

I actually work in the research department at our bank. We pull these items for customers all the time, but we do have a standard charge of $5 per copy/$30 per hour. Of course it a case by case decision whether we charge for this service or do it as a courtesy for the customer.