No. You paid for the use of tax preparation software. And you received your income tax refund. If the IRS chose to send you a check instead of a direct deposit, that was due to a decision made by the IRS or due to you entering wrong banking information and having to receive a check instead of a direct deposit.
From the IRS:
If you got a paper check instead of direct deposit, it’s because:
Who is the check from? The Treasury Dept or IRS or your state or the sbtpg bank?
"I paid for payout to be put into the bank..."
You did not pay any extra fee to have a direct deposit. If you paid a "refund processing fee" that fee was to have your TurboTax fees deducted from your federal refund instead of paying your fees upfront using a credit or debit card. There is never an extra fee for direct deposit. The refund processing fee went to the third party bank that received your refund from the IRS, extracted your TT fees to send to TT, took the $40 for itself ($45 in CA) and sent you the rest----either as a direct deposit or as a check mailed to the address on your tax return. The third party bank may have mailed a check to you if there was a problem with the direct deposit information you entered.