No. Your refund comes from the IRS. After Turbo Tax transmits your return to the IRS they are done with their part. They don't touch your refund.
If the IRS doesn't send your refund in a certain amount of time or reduces your refund, Turbo Tax still needs to get paid.
Were the fees supposed to come out of your refund?
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.
No --owing your fees to TurboTax does not stop the IRS from processing your tax return or sending your refund. The IRS does not know or care about your TT fees. However, if you chose to have your fees deducted from your federal refund, and it is taking a long time to receive the refund--see below:
Did you choose to have your TurboTax fees deducted from your federal refund? Is your refund taking an unusually long time to arrive? Or was your refund seized to pay a debt you owed? if so, you signed an agreement that says TT can withdraw its fees from your account. TurboTax would have sent several emails to you before they took the money out of your account.
IRS phone lines supported by customer service representatives for both taxpayers and tax professionals are not staffed at this time. To check on regular tax refund status via automated phone, call 800-829-1954. (This line has no information on Economic Impact Payments.)
TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer. Many refunds are taking longer during the pandemic.
Once your federal return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.
You need your filing status, your Social Security number and the exact amount (line 20 of your Form 1040) of your federal refund to track your Federal refund:
To track your state refund:
If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.
Turbo Tax says......
We understand that these are unprecedented times and we’re committed to helping our customers who are experiencing hardships. If you’re in need of assistance, call us by the Tuesday prior to your debit date at 1-888-808-1723 to speak with a trained specialist and mention “auto-debit”, or visit TurboTax Support.