Where do I enter a federal extension payment that I paid outside of the Turbotax software?

To enter, change or delete a payment made with an extension request (Federal, State, Local) -

Click on Federal Taxes (Personal using Home and Business)
Click on Deductions and Credits
Click on I'll choose what I work on (if shown)
Scroll down to Estimates and Other Taxes Paid
On Income Taxes Paid, click on the start or update button

On the next screen select the type of extension payment made and click on the start or update button

The federal extension payment will be shown on Schedule 3 Line 10. The amount from Schedule 3 Part II Line 15 flows to Form 1040 Line 31