There is no "refund processing" fee if you are not getting a refund. But if you used a paid version of the TurboTax software, you pay whether you are getting a refund or owe tax. The fee is for using the software; it is not based on whether you are getting a refund or how much the refund is.
How can I see my TurboTax fees?
If your TurboTax fees are higher than expected, you can reduce them by removing add-ons (BEFORE you e-file) :
Are you using the TurboTax desktop or the TurboTax online editions? Where are you seeing a processing fee?
Did you pay the tax due with a credit card? There may be a convenience fee.
How to pay a federal tax due
https://ttlc.intuit.com/community/tax-payments/help/how-can-i-pay-my-federal-taxes/00/26212