TurboTax does not issue refunds. If you selected to have your TurboTax fees paid from your refund, Santa Barbara TPG is who handles the transaction when you request to have your fees paid from your refund, you can check the refund status here: https://taxpayer.sbtpg.com/login. Once the IRS or your state issues the refund then you will receive it, the timing depends if you requested a direct deposit or a paper check. Typically there is not a delay once the funds are sent from the IRS to TPG for those funds to be released to you.
Please see this for more information: https://help.sbtpg.com/hc/en-us
Check your federal refund status here: Where's my Refund?
If you are anticipating a state tax return refund those processing times vary from state to state. To check on a state refund please visit your state Department of Revenue website.