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No, you didn't do anything wrong the earnings are taxable income and it will increase your AGI. Therefore, it is best to remove a little extra from the excess to avoid this loop.

You might be able to recharacterize the new excess as a traditional IRA contribution, make it nondeductible and then convert it to the Roth IRA (backdoor Roth contribution). If you don't have any other deductible traditional IRAs then this conversion will be nontaxable (only earnings would be taxable). You will have to request with your bank to have the amount recharacterized. 

You will enter the recharacterization when you enter the contribution to the Roth IRA:

1. Click on "Search" on the top right and type “IRA contributions”
2. Click on “Jump to IRA contributions"
3. Select “Roth IRA”
4. Answer “No” to “Is This a Repayment of a Retirement Distribution
5. Enter the Roth contribution amount 
6. Answer “Yes” to the recharacterized question on the “Did You Change Your Mind?” screen and enter the contribution amount (no earnings or losses)
7. TurboTax will ask for an explanation statement where it should be stated that the original $xxx.xx plus $xxx.xx earnings (or loss) were recharacterized.
8. On the screen "Choose Not to Deduct IRA Contributions" answer "Yes" (if you are thinking about doing a backdoor Roth. If you have a retirement plan at work and are over the income limit it will be nondeductible and you only get a screen saying $0 is deductible)

If you convert it to a Roth IRA in 2021 you will report this on your 2021 tax return:

1. Click on "Search" on the top right and type “1099-R”
2. Click on “Jump to 1099-R”
3. Click "Continue" and enter the information from your 1099-R
4. Answer questions until you get to “Tell us if you moved the money through a rollover or conversion” and choose “I converted some or all of it to a Roth IRA”
5. On the "Your 1099-R Entries" screen click "continue"
6. Answer "yes" to "Any nondeductible Contributions to your IRA?" if you had any nondeductible contributions in prior years.
7. Answer the questions about the basis and value

Please see What happens if I made a ROTH IRA contribution but my modified adjusted gross income exceeds the lim... for additional information.

@SWJohnson