Ditto TR on how to handle it but see below. If you don't want to give a letter, you can just tell them the bank will pay it.
Many banks absorb the credit report fee, for instance, but we still have to disclose it. If you would rather not go through all that crediting and assuming it's a 3rd party appraisal, on the HUD, you can just show it POC-L to the inside, carry it over to page 3, just like a Credit report fee and be done with it (and it's easier to understand by the borrower).
To pay for then reimburse would be paying twice.