There is no fee or advance direct deposit. The $40 fee was only the Refund Processing Service charge to have the fees deducted from your federal refund. It won't speed up your refund. In fact it may add a couple days to get it since it has to go through the 3rd party bank to take the fees out.
Did the IRS send your refund?
You misunderstood. There is no such thing as a 2 day advance deposit of your refund for $40. There is a $40 "refund processing fee" that allows you to pay your TurboTax fees from your federal refund instead of paying upfront with your own credit or debit card. Then a third party bank receives your refund from the IRS, takes out the amount you owe to TurboTax, keeps $40 for itself, and sends you the rest of the refund. That process does not speed up your refund at all. It can actually cause it to take a day or two longer for you to receive the refund.
How can I see my TurboTax fees?
https://ttlc.intuit.com/questions/2565973-how-do-i-review-my-fees-in-turbotax-online
What is Refund Processing Service?
Santa Barbara Tax Products Group, LLC (SBTPG) is the bank that handles the Refund Processing Service when you choose to have your TurboTax fees deducted from your refund. This option also has an additional charge from the bank that processes the transaction.
You can contact them SBTPG, toll-free, at 1-877-908-7228 or go to their secure website www.sbtpg.com
https://ttlc.intuit.com/questions/2580357-who-provides-the-refund-processing-service