Sounds like this 1099-G was for an overpayment of state taxes. If it is asking about unemployment, you are entering it in the wrong place.
A refund of state income tax goes under Other Common Income, not Unemployment. See the screenshot below.
If you itemized last year, then the amount reported on the 1099-G counts as income. If you did not itemize deductions last year, it will have no impact on your tax return. Either way, you should report it. If you tell TurboTax it was a refund of state income tax, and you used TurboTax last year, then TurboTax may realize whether this income was deductible, but it will probably ask you if you itemized last year.
