I don't mind regifts generally. Something that made it obvious something was a regift might give me a giggle but I don't think I'd say anything about it to the giver. Either it's a good gift for me, that happened to pass through someone else's hands first, or it's a thoughtless gift for me, that they had lying around instead of getting at the store fresh.
I'd keep the cash. Like GLaDOS says, if they didn't look at the thing closely enough to notice it, they give up their claim to it, IMO. This almost happened to me once, actually. I was given a book that I didn't want, so I took it to work and put it out on the table with a note saying, "Free, please take." No one had taken it by noon so I was glancing at it again as I ate lunch, and out fell a $5! Turned out the giver had stuck some cash in the pages for me. I shook the cash out and kept it, as it was originally meant for me and no one else had claimed the book yet; but, if someone had claimed it earlier and then told me they'd found cash in it, I would have laughed and said, "Lucky you! Keep it. I should look at things more closely!"
A check I would probably give back to whoever it was made out to, if possible, and with some discretion, but I wouldn't make up a story about finding it in some totally different place. They knew what they gave me was a regift, after all, no need to get awkward about it.