If you have not filed, you can simply remove the form by following these steps:
1. Sign into your account, select Take me to my return
2. To your right upper corner, in the search box, type in "1099g" and Enter
3. Select Jump to 1099g
4. On the screen, Review your 1099-G info, locate the correct 1099G and select the trash can to delete.
See the attached screenshot.