The refunds come from two separate taxing authorities, so they usually don't come together. I'm thinking you meant that you FILED your tax returns together; there is no additional charge for that.
So I'm not sure what fee you're referring to. Maybe you chose to have your TurboTax fees deducted from your federal refund? That's called the "Refund Processing Service", and the fee for that service is $34.99. That fee will not be refunded.
*** I am NOT a tax expert. I am a seasoned TurboTax user, and volunteer to provide assistance to TT users. Nothing I post is to be considered TAX ADVICE; I bear no legal liability for responses.***