Are we required to notify our customer(s) when we return a check drawn on their account(s) due to missing or improper endorsement? If so, which regulation does this fall under?

Customer A (your customer with an account at your bank, BigBank) wrote a check to JQ Public, who deposited said item in his bank, Bankofnobrains. Bankofnobrains did not check for endorsement and forwareded via normal FRB collection process. BigBank gets item, sees there is no endorsement, and retuirns the item for improper/missing endorsement. Customer A's account was never debited, so no need to notify the customer.

Does that sum up your question correctly?

Since Bankofnobrains has guaranteed the endorsement (or lack there of) why would BigBank return this in the first place unless the customer claimed that the correct party never received the funds? Sounds like BigBank is wasting a lot of time looking at check endorsements.

What he said. Looks like you may have misnamed the banks in your scenario.