My bank rejected my refund, do to a name mismatch, and stated that they returned the refund back to TurboTax
If your bank rejects your refund deposit it goes back to the IRS (or State) not TurboTax. The IRS (& State) will automatically switch you to receiving a check.
Unless you had your TurboTax fees deducted from your refund, it will bounce back to the bank that handles the transaction & they in turn would send you a check. You can go to the Santa Barbara Tax Products Group website if you need assistance with your refund.