Pretty sure the Deluxe service used to include the State filing and there was no additional "$40 processing fee". Now they hit you with Deluxe price +$39 for State + $40 for "processing fee".
The $40 processing fee is for the bank services used if you elect to pay the TurboTax software fees out of your refund. You can avoid this fee by paying with a debit or credit card.
There has always been a separate fee for state. And always been the Extra $40 Refund Processing Service charge (45 in California) to have the fees deducted from a federal refund. Or you can pay upfront with a credit card to avoid the extra charge. And then the refund will come directly to you without going through the 3rd party bank to take the fees out.
What is the Refund Processing Service
https://ttlc.intuit.com/questions/1900596-what-is-the-refund-processing-service
Remove Pay with Refund fee