First, the paying bank is generally liable to its customer for paying the altered item. It's properly payable only as issued (allowing for completion, if issued with payee or amount missing). Alteration of the payee or amount (and some would say date) is sufficient for your customer to ask for reimbursement for the full amount of the check (in the case of an alteration of the payee) or the difference between the amount of the check as paid and the amount as issued (in the case of an altered amount). There is no stated time period in the UCC by which you have to make the adjustment.
But the paying bank that's received such a claim should get an affidavit concerning the alteration, so that the paying bank can enter a warranty claim (without entry) directly against the depositary bank for breach of the depositary bank's presentment warranty under UCC 4-207 that the check wasn't altered.
Your customer has one year under 4-406 to make his claim of alteration against your bank (a shorter period may apply in some states or if the deposit contract provides for a shorter period). There is a three-year statute of limitations on your claim against the depositary bank (shorter in some states).
You may have defenses against your customer's claim of alteration. One such defense is lack of timeliness, although that would not apply in your situation. Another is contributory negligence (such as leaving so much blank space on the check as to facilitate the alteration). The repeat wrongdoer rule in 4-406(d)(2) can also limit your liability to your customer in the case of multiple altered checks. And you are generally protected from your customer's claim of an altered amount if the check was issued with the amount omitted, and it was completed with an unauthorized amount.
The depositary bank is generally protected from your warranty claim against it if you had a defense against your own customer and failed to exercise it.
You'll find
The Check Book, available at
http://www.bankersonline.com/tools/training/ucc3_4trng_ge.html in the BOL Banker Store for free download, a valuable resource for information on who's responsible for check problems like this one.