Your tax refund would have been direct deposited by the IRS into the account you entered when completing your tax return.
To review the bank routing number and account number you entered -
On the Filing Instructions page of the tax return
On your Form 1040 Lines 35b and 35d
On the Federal Information Worksheet Part V
TurboTax does not receive any kind of tax refund, federal or state.
Or did you request to have the TurboTax account fees paid from the federal tax refund?
If you requested to have the TurboTax account fees deducted from your federal tax refund, the IRS will send the refund to a third party processor to have the fees and the $40 service charge deducted. The third party processor will deduct the TurboTax fees plus the $40 service charge and then attempt to direct deposit the remaining refund balance into the account that you entered on your tax return.
For the status of your tax refund you will need to contact the third party processor, Santa Barbara Tax Product Group, using their website - https://www.sbtpg.com/
Tax Products Group Contact Information - https://help.sbtpg.com/hc/en-us/articles/230084587-Contact-Information
Call 1-877-908-7228
Or email - TPG-CSsupport@greendotcorp.com