First, if you work remotely because the company wants you to, you are not subject to NY income tax. There is no reason for them to withhold state tax unless they are not willing to inform themselves or they are too lazy to handle employees based on their individual needs.
If you work remotely because you want to (but the company would have a place for you if you moved to NY) then your tax situation is more complicated. If you never set foot in NY, then you don't owe NY income tax. But if you work in NY for even one day (such as, you are required to attend training or orientation or occasional meetings on site) then all your income from that employer is subject to NY state income tax.
Since you had NY tax withheld (whether rightly or wrongly), you need to file a New York non-resident income tax return. Turbotax will ask you to allocate the amount of your income that is New York-sourced. None of your other income is from NY (bank interest, investments, etc.). Your wages are from NY if you worked in NY state even one day, but if you never worked in NY state, then your NY wages are zero. If you allocate zero NY wages, then your NY tax return should claim a full refund of all your NY withholding.
Be prepared to prove, if asked, that either:
a. you are working remotely because your company requires it, or
b. you are working remotely for your own convenience but you never physically lived or worked in NY state for all of 2023.
