No, legally TurboTax can not deal with your refund or stimulus. There are two options.
1. If you paid for your tax preparation when you did your taxes, the stimulus will deposit or mail the same as your refund straight from the IRS.
2. If you had your tax preparation fees taken out of your refund, then you opted to have SBTPG as an intermediary. The bank, SBTPG, charged you an additional fee to take out TurboTax fees, receive your refund, and deposit it into your account or give you a debit card.
If your federal refund went to SBTPG, they could get the economic impact payment as well and it could then be routed to you which caused a short delay.
Please see: Is My Second Stimulus Check on the way? and the IRS stimulus website