Since TX doesn't have a state income tax I will assume you mean the Federal refund ...
Turbo Tax only gives you an estimated date. The IRS usually pays most refunds within 21 days. But these are not normal times. This year is taking the IRS longer to send the refunds. There are millions more people filing returns to get the Stimulus payment.
See this news article on Refunds being delayed
Only the IRS can tell you. If your return was Accepted then check IRS Where's my refund
When will you get your refund?
IRS - Questions about Refunds
From this IRS website - https://www.irs.gov/newsroom/irs-operations-during-covid-19-mission-critical-functions-continue
As of May 15, 2021, we had 300,000 individual tax returns received prior to 2021 in the processing pipeline. Including current year returns, as of May 15, 2021, we had 16.4 million unprocessed individual returns in the pipeline. Unprocessed returns include those requiring correction to the Recovery Rebate Credit amount or validation of 2019 income used to figure the Earned Income Tax Credit (EITC) and Additional Child Tax Credit (ACTC). This work does not require us to correspond with taxpayers but does require special handling by an IRS employee so, in these instances, it is taking the IRS more than 21 days to issue any related refund. If, as a result, a correction is made to any RRC, EITC or ACTC claimed on the return, the IRS will send taxpayers an explanation. Taxpayers are encouraged to continue to check Where’s My Refund? for their personalized refund status and can review Tax Season Refund Frequently Asked Questions.
Are they asking you to pay the fees? Sounds like the IRS is taking too long to send your refund or reduced it. See What if the IRS reduces your refund or delays it.
Then when the IRS does send your refund they won't take the fees out again.
And, Why you got charged,
You should have received about 4 emails asking for the fees. If you don't pay they will debit your account. You had to agree to it.