A consumer RE loan is collateralized with the primary residence and deposit collateral. The consumer is requesting release of the deposit collateral, as home improvements were made on the home and they are confident of the increase in home value.
What are the bank's options? Bank would like an appraisal to substantiate the value in order to release, but how to charge/disclose the appraisal fee to the customer?

There would be no formal disclosure necessary. You would tell them the process, your requirements and the costs involved for you to consider releasing the additional collateral. They either agree to pay it or they do not.