Since there is an amount in box1 of the Form 1099-G then the state of Virginia has said that the income received by you was unemployment compensation. If this is incorrect then you need to contact your state and get a corrected Form 1099-G so that the income is reported in box 2 as a state tax refund.
A copy of the Form 1099-G is sent to the IRS so they will expect to see this income reported on your federal tax return as unemployment compensation on Schedule 1 Line 7 and on Form 1040 Line 8.
