There is something fishy, the insurance company pays less, and the repair shop is unwilling to repair it. You can change it directly to the repair shop for repair. Agree to fix the loss (just give some benefits to the loss-making operators). They won't close the case if you don't agree.
If you fix the damage, invoice and settle the claim, there is nothing you can do.
Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.