they can get your old mortgage lien released in time for things to go through for you. That's your leverage over them (assuming you did the smart thing and purchased an owner's policy and not just a lender's policy for your bank).

If you didn't purchase an owner's policy, and all that exists is a lender's policy, then you can notify your lender that the title company didn't do their job and get the old lien released. The bank won't like that situation, and they can threaten to make a claim on the lender's policy.

That's your leverage. As NorthBayCoug says, getting the old lien released at the closing where you refinanced is one of the major jobs that the title company was supposed to take care of. The schedule of exceptions on the title policy would have shown the preexisting mortgage. Your new lender that you refinanced with would NOT have accepted that exception, and they would have required that lien to be released.