After you file

Your post is confusing.  SBTG is used when you have your TT fees deducted from your refund.  But it does not get involved if you asked the IRS to mail you a paper check (or the IRS chose to do so for some reason), since that check goes directly to you from the IRS.  Did the IRS say your refund was Sent, or that it was Mailed?  If the latter, only the USPS controls the timing at that point.  And you would still owe TT its fees.