You won't pay taxes on the nondeductible contribution later as long as you properly track your basis in nondeductible traditional IRA contributions. Your basis is tracked on Form 8606. When you take a distribution, your basis is applied proportionately on Form 8606, reducing the taxable amount of the distribution. You'll always have some basis until you have a zero balance in traditional IRAs.
If you have not yet filed your tax return and did not request a filing extension by April 18, 2022, the deadline for obtaining a return of this contribution before the due date of your 2021 tax return has passed. Otherwise, if you choose not to have to track basis in traditional IRA contributions and you want to obtain a return of the contribution before the extended due date of October 17, 2022 as I mentioned previously, the contribution will be treated as never having been made. In 2021 TurboTax you'll omit the contribution, then enter a code P (along with code 1 if you are under age 59½) 2022 Form 1099-R with the IRA/SEP/SIMPLE box marked. When asked, be sure to indicate that it's a 2022 Form 1099-R . Box 1 will show the gross amount of the distribution (amount returned adjusted for gain or loss) and box 2 will show the investment gains or zero if there was no gain or there was a loss. This will cause TurboTax to prompt you to enter an explanation of the return of contribution where you'll indicate the amounts and dates of the amount contributed, the amount returned, and the adjusted amount distributed.
Decline having any taxes withheld from the return of contribution.
(If you've already filed your tax return, you'll need to prepare an amendment (Form 1040-X) and at the top write "Filed pursuant to section 301.9100-2." You'll need to file Form 1040-X along with a manually prepared Form 8606 showing that your nondeductible traditional IRA contribution was zero instead of what was reported on the Form 8606 originally filed with your tax return. TurboTax will not prepare the necessary corrected Form 8606.)
