No don't enter it as a quarterly estimated payment. But it does go in the estimates section.
Make sure you enter it on your return. It will show up on 1040 line 26 with estimates paid. It will either add to your refund or reduce your tax.
If it didn't transfer over from last year then enter a refund from last year that you applied to this year here. BUT first make sure it's not already there. You don't want to apply it twice.
Federal Taxes
Deductions and Credits
Then scroll way down to Estimates and Other Taxes Paid
Income Taxes Paid - Click the Start or Update button
Next page scroll down to 2019 Refund Applied to 2020
Click Start or Update by the tax you applied
