The insurance company behind the Chase card benefit will not get into the discussion between you and your rental company. You have to resolve the final settlement, preferably charge that to your card and then submit everything you have to the insurance company. They will check things and often ask a few more questions and for things you have already submitted. If the settlement was charged to your credit card they will pay the amount onto the credit card. If it had to be paid by bank transfer they will send you a check or credit it to the card.