What is recoverable depreciation?

Are you obligated to hand over the check for the recoverable depreciation to the roofing company? Insurance company has issued a big initial check which is to be given to the roofing company however, they refused to pay the companies Overhead and profit in the claim. The contract we have with the roofing company is actually less than what their estimate because it is minus our deductible which we are financing. Are we obligated to give them this even though the contract balance shows only $600 something left remaining? Their estimate was more.