We have a customer that gave us their intent to proceed. The customer paid the appraisal fee and we ordered an appraisal. The appraisal was completed and we gave it to the customer. The customer withdrew the loan.
Can we keep the appraisal fee or do we need to refund to the customer?

Keep it

They applied, gave consent and paid. Bank ordered and paid.

Customer did what they were supposed to do, so did bank. The fee offsets the cost of the appraisal the customer wanted and intended. It's yours

The only reasons to refund it would be any agreement by the bank to refund all costs for loans not consummated (not many banks promising that!) or a state law requirement.

Just to piggyback, what if the borrower did not give their intent to proceed, but the bank ordered an appraisal and the appraisal was completed. If the bank reused that appraisal, could they pass the fee for the appraisal on to a new borrower purchasing the property?