A release is usually the final word. Whatever occurred between you and your landlord before the release is out of reach. An oral promise that contradicts the provisions of the release is not acceptable evidence in a New York court.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
it's not worth it. It is possible to void the written agreement if you can prove that it was signed under duress - a very steep hill to climb. The legal fees alone would be more than the security. As Mr. Smollens stated, you can not change a written agreement orally.
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Is it hypothetically possible to get the deposit based on verbal modifications to a contract? Yes.
Is it easy to do? No, and you will end up spending more in court costs than the deposit is worth.