You would have to file a nonresident New York return for 2020 and 2021 to have the taxes withheld refunded to you. You may need to do so for 2019 as well if New York taxed any retirement distributions after you moved. For 2021, you would allocate $0 of the retirement distribution to New York in the nonresident New York return. You would also allocate $0 of any other form of income, assuming you did not earn any New York-sourced income. This should result in a full refund of the New York state taxes that were withheld in Box 14 of Form 1099-R.
You would need to amend your New York 2020 return to have those taxes refunded to you if any were withheld. If you did not originally file a New York return in 2020, you still can to get this amount refunded. Please note that depending on the size of your pension, you may have to amend your Georgia return as well. If you received any credit on your Georgia return for taxes paid to New York, you would no longer be eligible for that credit if you apply for a full refund from New York of taxes paid. If you received a credit for taxes paid to New York in 2020, it would show up on your 2020 GA Form 500, Line 18.
