There is not a tax refund fee for a state tax return.
What you are seeing is the cost of the state program ($50) when using the TurboTax online edition of Deluxe or higher.
See this TurboTax support FAQ for checking your fees - https://ttlc.intuit.com/community/charges-and-fees/help/how-do-i-review-my-fees-in-turbotax-online/0...
See this TurboTax support FAQ for removing fees - https://ttlc.intuit.com/community/charges-and-fees/help/what-can-i-do-to-reduce-my-fees/01/26051
