You will need to file an amended tax return and include the 1099-G.
Amends in TurboTax will be available on March 25.
Do not amend until your original return has been processed. When you start your amend, TurboTax will show your refund amount as zero. Then that amount may change as you amend your entries.
When amend is ready, go into TurboTax and follow the instructions for amend. The new stimulus bill will give federal income tax forgiveness for up to $10,200 in last year's unemployment payments.