Uh, yes I ask customers to sign refund receipts. And then I put them in the till box so they can go to our sales media records at the end of the day. Yes, you need to keep them. It's documentation.

They should be signed by the customer but if you are too lazy for that at the very least a shift should be signing them before they make it into the sales media envelope. Understand that when you do a refund you remove money from the business. What the signed receipt tells you is that the money made it to the customer and didn’t get stolen.

Yes it does matter if you keep them. At my last store, we didnt have customers sign them but it might be different at every store. At the very least you should be putting them into the til drop box (where the 20s go) so the SSV can sign it and put it in the proper envelope.