I have never been charged a transaction fee for eFiling Federal taxes. I use the desktop version of Turbotax, so I have already paid for the program. I use the ACH pay from my checking account payment method. It costs $25 to eFile State taxes, but I got a $10 discount when I bought TurboTax at Costco. You need to find out who is charging the transaction fee - the IRS, your bank card, etc.
I hope this helps.
