They are going to fix your home. The fact that you have a mortgage and what amount you owe is not really at all relevant to any of this to the insurance company. The insurance company is contractually obligated to repair the damage and pay a contractor to fix this issue.
A pipe bursting can be pretty expensive to get resolved. It damages floors as well as walls where the pipe either burst or leaked down through. If it damaged half the house that means they have to tear out a whole lot of flooring and walls to get rid of all the damage. They also need to make sure everything is completely dry so that mold doesn't start forming, especially black mold which can very much harm the health of any occupants including pets.
The insurance company is never going to forward the money to the mortgage company and then let the damage just continue to exist. It's their job to make sure to have the damage repaired. Also, their customer is you, the owner of this property, and not the mortgage company to which you owe money. You are the named insured on the insurance policy and they can't simply send money to the lender instead of you.