You enter this as follows:
Go to:
See the "learn more" link of turbotax on the "Federal Itemized Deduction Taken As State Income Taxes For Donation Made To Qualified Rural Hospital Organization" page.
It indicates that you enter it as GA estimated taxes. Full text reproduced below.
"If you made a donation in exchange for a state tax credit and claimed itemize deductions on your Federal return, your Federal return charitable contribution deduction must be reduced as a result of receiving or expecting to receive this state tax credit. You may qualify for a safe harbor that allows you to treat some or all of the disallowed charitable contribution as a payment of state and local taxes. Remove any disallowed charity donation from your Federal Schedule A and enter your safe harbor amount as an estimate paid to Georgia on the Federal return. Return to this screen and enter the amount claimed as Georgia Estimates Tax Payments. If you do not claim the state tax credit for this donation, you may continue to claim the charitable deduction on your Federal and Georgia return."