I'm not sure you answered the questions. You need a W2 that reports what your employer actually did (whether it was correct or not). The W2 is just letting the taxing agencies (and you) know who they paid taxes to from your pay. Again whether the withholding was correct or not doesn't matter. You will use that information to complete your tax return to calculate what taxes should be paid to the corresponding state and be refunded any amount of overpayment.
So if your employer paid taxes to GA from your pay hopefully the box 17 that corresponds to a box 15 GA shows that and then you can file a tax return to get those taxes refunded.
If however, the employer did not pay taxes to GA from your pay then there will not be a GA box 15 with a corresponding box 17 amount and you will not need to file in GA.
Having said that, if your employer actually paid taxes to GA from your pay but there is no W2 line with GA box 15 and a corresponding box 17 amount then you have nothing to get refunded according to that W2.
Once you have a correct W2 that shows what amount of taxes from your pay were actually paid to what state you can complete and file your tax returns in those states to reconcile and get whatever taxes were overpaid, refunded.
You will enter the information from your form W2 in the federal "Wages & Income" section. Then in the state interview you will allocate wages according to your residence and work states.
Assuming you did not physically work in GA for that GA employer and you were not a resident of GA, then you would allocate zero wages to GA. Any taxes withheld and paid to GA shown in box 17 with GA in box 15 will be refunded.
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