They likely do have a valid security interest in the ring. They sold you the ring, not the diamond ("You grant us a purchase money security interest in each item of merchandise purchased on your Account to secure its unpaid purchase price....")

You can attempt to negotiate a lesser payoff (the band is probably only "worth" salvage value - being melted down and turned into a new piece of jewelry). If they agree to a settlement of the debt, be sure that it covers all claims and get the agreement in writing before you pay.