Incorrect state tax withholding

I got a promotion from local to national. When Payroll processed my promotion, they incorrectly recorded that I lived in Georgia. I do not and have never. I live in Washington state and have no state income tax. I found out when I was told I was getting a region-based pay increase since I live and work in WA. 

I just got my W2. They have withheld or paid a significant amount to the state of GA in state income tax. I have never lived or worked in GA. I contacted Payroll and their reply was "Why didn't I catch this earlier?" 

What do I need to do to get the taxes paid to GA back?

Thank you!