Sadly the fees are not a secret ... they are presented to you all the way and if you did not want to pay the extra fee for the convenience of having the other fees withheld from the federal refund then pay with a CC instead.

If you have not yet filed : 

How to see your fees
https://ttlc.intuit.com/questions/2565973-how-do-i-review-my-fees-in-turbotax-online   

For help with fees 
https://ttlc.intuit.com/questions/1901213-what-can-i-do-to-reduce-my-fees   

How to remove the Pay from your Refund fee 
https://ttlc.intuit.com/questions/1900517-how-do-i-remove-refund-processing-fees-in-turbotax-online-... 

If you have filed : 

What did I pay last year for TurboTax?

When you begin your return using the Free Edition, it will be free unless you are required or choose to upgrade.

Only very simple tax returns can be completed using the Free Edition. When you choose to upgrade, TurboTax advises you on the screen how much the upgrade will cost. They may not advise you that there will also be a fee for a state return when you upgrade. Here is a current price listing for each online version: https://turbotax.intuit.com/personal-taxes/online/

There is also a completely free website if you qualify which is free for federal and state.  And has more forms than the Federal Free Edition, like Schedules A, B, C , D, E, F, EIC, H, K-1, SE,  etc.

NOTE:  You will have to log out of  your regular Turbo Tax account and setup a new account with a new username and new password or it will take you back to regular Turbo Tax.

To qualify for the Free File website  you just need to meet one of these 3 things 
AGI $34,000 or less
Active duty military with AGI of $66,000 or less
OR qualify for EIC (earned income credit.)

In order to use the Free File program, you have to start it at a special website.  Click on the bottom Orange button I Qualify Start Now and set up a NEW account or it will take you back to regular Turbo Tax.
http://turbotax.intuit.com/taxfreedom