Yes, the customer has a deadline to notify their bank. It can vary from one year (per the version of UCC 4-406 that Randy provided) to as little as 180 days in Florida or 60 days (!) in Georgia. So know what the UCC says in your state.
Your bank should get an affidavit of alteration from your customer. Your bank can then file a claim against the depositary bank for breach of the presentment warranties in UCC 4-208 (the depositary bank warrants to the paying bank that, among other things, the check was not altered). But you cannot make such a claim if you give your depositor a break and reimburse them when their claim is late under 4-406.
UCC 4-406's time periods can be shortened by appropriate language in your bank's deposit account agreement. Check with bank legal counsel before trying to insert such language to make sure it will be effective in your state. Courts sometimes determine that such deadlines in deposit contracts are unreasonable.
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