Answer:
If the check in question was issued by your depositor, I don't think there's added risk. But if the check issuer is not your depositor, it's possible the issuer intended for the check to be used for another purpose, such as a payment on the check issuer's loan at your bank, or to purchase a cashier's check.
As a general rule, a bank should not accept a check payable to the bank itself for any other purpose than to pay an obligation owed to the bank.