"overpaid" by employer. Do I have to pay it back?

I have been working for a temp agency that just caters to one company for the past 2 years. The first assignment I made $17/hr and the second one I made $19/hr. The third assignment my rate remained at $19/hr. I have been working that assignment for over 6 months and doing an excellent job. However, this week the agency called me and told me that this assignment should only pay $13/hr and they had already corrected it on my previous check and I might have to pay the rest back. This would amount to close to 6K as I worked a lot of overtime! Can they legally do this? I was not aware that I was supposed to be being paid $13/hr for this assignment.