The question is "How does Salvage work"
This is the simplest answer. When a vessel is lost, one of 2 salvage contracts is signed. Note I said contracts, not handshake agreements. One of those contracts is called a Lloyds open form. This is the form that all salvage contractors dream about, and this is the one your divers think that they have. It's closely related to "Finders, keepers". Lets say an item is lost at sea. the salvage company gets the owner to sign a Lloyds open form contract, and the item now (kind of) belongs to the salvors, as do the liabilities. If the item lost explodes and kills turtles, the salvor goes to jail. When the salvor safely delivers the sunken item to a safe place (it has to float on it's own for 24 hours, or be placed on the hard), the salvors submit their expenses and reasonable profit to the owners and negotiate for salvage costs. The salvors own the item until negotiations are complete.
The other salvage contract is known colloquially as the "BoatUS" contract. If you ground, run out of gas, take water, whatever, and you call BoatUS, they will make you at least verbally agree to a salvage contract worth 10% of the value of the item, and make you sign a standard BoatUS form before giving you a pump, line, or tank of fuel. They are again responsible for your item (usually a boat) until it is in a safe place, or you release them from their services. Lets say you ground. They will be happy to tow you off. Before they put a line on your boat, you will sign a BoatUS salvage contract promising them 10% of the value of the vessel, or an hourly rate. Once they float you, you may be towed back to a safe harbour or continue on on your own, or be cited by the folks responsible for the health of the sea bottom in your area.
What you have is a pig in a poke. You verbally agreed to pay a salvage to 2 salvage divers. You showed them where the ring was, and they found it. Legally, it's finders keepers. Now, you have negotiated a rate of $2100 for the return of the ring. You likely did all of this without the knowledge and consent of the insurance company, therefore they are under no obligation to refund you the $2100. They may have a dive team on retainer who would have recovered the ring for say $500 flat fee plus a monthly retainer. so. You contracted for a service. You are now obligated to pay for the service. If you choose not to pay for the service you contracted (a verbal agreement is as good as a written contract when they hold the ring) they have every right to file a lien against the property and gain ownership of it. Once they own it, they may sell it to you or to anyone else.
That's how salvage works.