A reclearing fee assessed in combination with a chargeback fee does raise the possibility of some UDAAP concerns, but under the appropriate circumstances it arguably would be defensible.
To clarify the terminology for these fees, which is not consistent across financial institutions, your institution charges a fee (which you call a “chargeback fee”) when a check deposited by a customer is returned for insufficient funds. This is commonly referred to as a returned check or NSF fee (for example, in Regulation DD, Official Interpretations, 12 CFR 1030, Paragraph 11(a)(1), Comment 3). You have told us that you charge this chargeback fee only one time, after an attempt to reclear the check and the drawee bank returns the check a second time. Provided that the chargeback fee is properly disclosed in your account agreements and otherwise is within the bounds of applicable regulatory guidelines, we do not see a problem charging this fee.
However, there arguably could be UDAAP concerns in charging a “reclearing” fee in connection with the second submission of a check for which a chargeback fee also will be assessed. Charging the reclearing fee after the first presentment fails in combination with charging a returned check fee after the second presentment fails could be argued to be a confusing and deceptive practice. In other words, the reclearing fee might be considered to be the equivalent of charging a second “chargeback” fee for the same check, with the only difference being a different name for the fee. We are not suggesting that this should be the case (the reclearing fee relates to the check returned after the first presentment and the chargeback fee relates to the check returned after the second presentment), but the bank could be susceptible to the argument nonetheless.
As you note, the bank makes the decision to reclear the check without asking customers whether they want to reclear the check and incur the fee. Conceivably, you might mitigate the UDAAP risks if your account agreement permits this reclearing fee and clearly discloses it as distinguishable from a chargeback fee if the check is returned a second time, and your institution has documentation describing the extra work that demonstrates the need to charge this fee, in addition to the returned check fee. However, as you suggested, it may be advisable to charge the reclearing fee only if a customer requests that your institution reclear the check.
Ultimately, the decision to charge both fees will be a business decision that weighs the advantages against the risks, and you may wish to consult with your bank counsel for a further analysis of those risks.