The answer is "it depends." A regular distribution made now would be subject to reporting on a 2021 Form 8606 to determine the taxable amount of the distribution and the taxable amount would be subject to an early-distribution penalty on your 2021 tax return.
To avoid all of that, you would explicitly request a "return of contribution," not a regular distribution. The distribution of a return of contribution is required to be accompanied by any investment gain or loss in the IRA while the money was in the account. If there is a gain, the gain will be subject to tax and an early-distribution penalty on your 2020 tax return.
If your modified AGI for the purpose allows you to be eligible to make a Roth IRA contribution you could recharacterize the contribution to be a Roth IRA contribution instead.
Even though you do not get a deduction now for the traditional IRA contribution, you are still saving for retirement if you leave the contribution in, the primary reason for contributing to an IRA. This money will not get taxed twice.
