Your institution (like most) makes a risk based decision to not review every check that clears your bank. However, the duty to identify and return a forgery by your midnight deadline rests with your institution. The bank of first deposit has know way of knowing if your customer wrote the check or not.
Unless you and the bank of first deposit are part of the same clearinghouse and have a contract to share liability, your institution is on the hook for any checks not returned by the midnight deadline. If you send them back through the Fed, the bank of first deposit can make a claim of late return and send them back to you.
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