Why am I now being charged two separate fees for this service? I want to remove one of them!

Federal Deluxe is $60.  A state return is a separate $50 so it must not be for state.  If you want the $60 deducted from your refund there is a $40 Refund Processing Service charge which you can avoid by paying with a credit card.

How to see your fees

https://ttlc.intuit.com/community/charges-and-fees/help/how-do-i-review-my-fees-in-turbotax-online/00/26353

For help with fees

https://ttlc.intuit.com/community/charges-and-fees/help/what-can-i-do-to-reduce-my-fees/00/26051

How to remove the Pay from your Refund fee

https://ttlc.intuit.com/community/downgrading/help/how-do-i-remove-pay-with-my-refund-fees-in-turbotax-online-and-change-my-payment-method/00/25880

If you chose the option to have your fees paid from your federal refund, there is an additional $40 processing charge to use that optional service. You would have been advised of that fee before you agreed to use the service.