If you're using a gift receipt type of thing then I highly doubt it would show. My gifts that I got via Amazon that were listed on my Babylist registry all had gift receipts, you should be good to go as long as it's a gift receipt (edit: pushed the button too soon, oops)
It shouldn't return to them, it should just be returned to a gift card so they shouldn't know.
They will not find out.. I returned a few things also.. just a gift card balance to you.
I think they would know because money would be refunded to them