Does TurboTax receive my refund after the bank rejects it?

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.

Yes I did have my TurboTax fees deducted from the refund.

Then your refund will go back to the Santa Barbara Group, they will issue you a check for your refund.  You can click on the link I gave you above for information about your refund.