A flea market is a little different from a house, where there's a record of ownership. Not exactly a "grab bag", now is it?
It may be true that someone has made their peace with losing the ring, but wouldn't it be nice to find out that someone was somewhat altrustic and tried to contact you when they found it? You have NO idea what that ring is--possibly a family heirloom or of high sentimental value. It wouldn't take THAT long at all to find the owners--possibly only a few hours. If it turns out that you can't find the people--at least you tried.
Killarney Rose, doesn't your title have the name and address of the previous owner? Maybe that's on a state-to-state level.