You mentioned that TurboTax added the excess amount to your taxable income. This implies that you made an excess contribution through your employer and your HSA contributions were reported with code W in box 12 of your W-2. This means that correcting the excess contribution to avoid an excess-contribution penalty required a return of contribution paid to you. The fact that you had the HSA custodian apply the resulting cash as part of your 2023 contribution rather than paying it directly to you does not change the fact that you received a distribution from the HSA (a "withdrawal" as TurboTax calls it, but that's a poor use of the word). Due to the requirement that the distribution include any investment gain or loss attributable to the excess contribution being returned, the amount of cash contributed for 2023 is likely a bit different than the amount of contribution that was returned.
Note that even though the excess was returned, the excess is still includible in your 2022 income because it was excluded from the amount in box 1 of your 2022 Form W-2. The purpose of obtaining the return of excess contribution was to avoid a 6% excess-contribution penalty for 2022, not to exclude the excess from taxation on your 2022 tax return. When you report in 2023 TurboTax the amount of cash distributed from your HSA as a personal contribution for 2023 you'll receive a deduction for this contribution on 2023 Schedule 1.
Do not change the code-W amount in box 12 of TurboTax's W-2 form.
