I'll ignore the reason for the change in AGI other than to say that if you are now eligible to make the Roth IRA contribution, you have until July 15, 2020 to do so. Your contribution returned before the due date of your tax return will be treated as never having been made, other than the fact that the earnings that accompanied the distribution are subject to tax and to early-distribution penalty. Keep in mind, though, that once the earnings distributed with the returned contribution are added to your tax return as described below, your AGI will increase by the amount of the earnings, so make sure that you are still eligible to make the Roth IRA contribution.
The earnings are reported on your 2019 tax return (form 1040 line 4b and on Form 5329 Part I) by entering the code JP 2020 Form 1099-R that you will be receiving near the end of January next year. Assuming that you had no taxes withheld from this distribution, you can enter into 2019 TurboTax a dummy Form 1099-R showing the amount returned plus earnings in box 1, the amount of earnings in box 2, and codes J and P in box 7, making sure to indicate in the follow-up that this is a 2020 Form 1099-R. You can then ignore the 2020 Form 1099-R when you actually receive it.
To eliminate excess shown in Form 5329 Part IV, revisit the Traditional and Roth IRA Contributions section and, when TurboTax indicates that you have an excess contribution and asks how much you had returned, enter the amount of contribution returned (not including earnings). Continue until TurboTax asks you to prepare an explanation statement for your return of 2019 contribution before the due date of your 2019 tax return.
The way to have gotten your intended result would have been to request a regular distribution in 2020 and not to mention anything to the IRA custodian about an excess contribution. You could have also gotten the desired result by waiting until after October 15, 2020 to request the distribution, the date after which the custodian is not permitted to process it as a return of contribution before the extended due date of your 2019 tax return.
