It's not worth fighting with your employer about it. It will all get straightened out when you file your Georgia tax return at the end of the year. The withholding is not the final tax that you pay. It's just an advance payment towards your actual Georgia tax for the year. When you prepare your Georgia tax return you will specify how much of your income was for the time that you worked in Georgia. The tax return will calculate the Georgia tax on that income, and you will get credit for the Georgia tax that was withheld. If the amount that was withheld is more than the actual tax, you will get a refund of the excess.
