No, it doesn't sound like this is taxable income to you.
If the former employer refunded something that would affect your tax return, they are required to send you a tax form that helps you figure out how to report the amount.
For example if the amount is additional wages, they are required to send you a corrected W-2.
Either way, you would only need to file a New York return as a nonresident if your NY income were $4000 or more.
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