Why did the insurer hold back part of my home repair money, and why is the check made out to my mortgage company?

Two checks, not one. TDI says that with a replacement cost policy, most companies pay in two checks. The first comes after the adjuster has seen the damage. It is the estimated cost of repairs, minus depreciation and your deductible. The company pays the money it held back for depreciation after it gets the bill for the finished job. TDI also says you usually must finish repairs within a set time, and to ask your agent or adjuster how long you have [1]. That is why the first check looks short: the holdback is the depreciation, and the bill for the finished work is what releases it. Keep the invoices.

Personal property works the same way. TDI says that with replacement cost cover you get two checks. The first is the actual cash value of the items. After you have replaced an item, the company pays the rest of your claim amount [1].

The mortgage company's part. TDI says that if you owe money on your home, the company will make the repair check out to you and your mortgage company together. You endorse it and send it to the mortgage company. In most cases the mortgage company deposits it, then releases money to you as the work is done. It may first ask for a list of the work, cost estimates, who is doing the work, and timelines. After it gets that information it must release all or some of the money to you within 10 days. If it does not release the money on time, TDI says to complain to the Texas Attorney General's Office [1].

Read your own policy for two things. Does it pay replacement cost? And how long do you have to finish repairs? The numbers and the agency names are Texas ones.