California is the only state as far as I know that in any way protects employers from recouping overpayments of wages if it is their fault and there they just have to sue you to take the money back. In GA, they can and will sue you if they please and in a some cases, they can simply deduct the wages from your checking account if you were paid by direct deposit as long as they let you know ahead of time that they are going to do it.

I'm an accountant and I have paid salaries to employees for a long time. I have deducted an overpayment from someone's account before, they were a current employee but it's the same thing, and I was very sure I was in the limit of the law to do so.

I would find the exact law but the GA DOL website is down. Feel free to call them, they will tell you that you have to pay it back.

And if you don't pay it back, you better be damn sure they can't prove it because all they have to do is take you to small claims court, show the judge the proof and then you will have to pay it.