You can absolutely get your stimulus deposited to your Turbo Card; but if you had fees/an advance, then there's a good chance the IRS doesn't have the information for your card. You'll need to go to the "Get My Payment" and manually enter the routing # and account from your card (you can find it on your 1040, page 2 also). From everything I understand, it's because a number of refund payments were sent to Santa Barbara Tax (who Green Dot owns), rather than directly to your card, if you applied for an RAL or had fees taken out. I say "a number" because it also appears some people got their refunds directly on their cards anyway, despite having an RAL/fees taken out. Either way: Check the Get My Payment page, manually enter the information for the account you want, and you should be good.
