@user04265 While New York is very aggressive in taxing remote work, your income that is "New York sourced" in theory appears to fall outside of their statute. First, the income is not performed on behalf of a New York employer, nor is it earned within New York state, and you are neither a New York domiciliary or statutory resident. Based on all you state, you simply don't file a New York return. If New York claims that the income is taxable to New York state, you will present all of the evidence you state to them as proof that while you performed the work for a New York company, you did not do so sourced to New York state and you don't pay tax there.
That is the real reason why you will not file a New York return, and not that it is $4500 in question. If the income is sourced to New York, then New York can tax the income if your overall income is $8000 or more ($16000 or more if Married Filing Joint). But facts and circumstances are that the income is not New York sourced.
You seem to have a legal mind, so the following link is the statutory language that New York uses to determine when income is "New York sourced": New York source income for nonresidents
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