Don't think there is anything to question. You got permission to hunt there, because the owners trust you, thing you are of decent character. You are hunting there frequently, so the must be a few spectators, that you find more than a few pennies and pull-tabs. Wedding rings, and jewelry, often carry a greater value, than the purchase price. If you can return them to the owners, it will mean a lot to them, the property owners, and anyone familiar with the story. You'll be a local hero to some, and it could only help you gain access to more spots to hunt, maybe a little leniency with the local law enforcement as well. Right now, you are sort of a suspect, metal rings, metal detector. The reward for honesty and a good deed, is much greater in this case, and you've been offered an opportunity to show these people what you are made of.
Now, you don't have to pull out you box of finds, and let them pick out the ones they like best. Should be some receipts, wedding photos, or some sort of proof. I'm also a skeptic, too many people trying to scam a dollar these days. Could be somebody who saw you dig up a ring, and wants it their self.
We've all been there ourselves, and have known many, who have lost or misplace something of value or importance, the frantic, desperate search, disappointment, and despair. You know how good it feels when a lost item is found or returned, after a long, empty search, and it will feel just as good, almost heroic, when you do the right thing. There is plenty of treasure out there to be had, couple of rings aren't going to make or break you.
