Does email from turbo tax saying thank you for choosing them to do your taxes mean they got their fees

Did you choose to pay your TurboTax fees out of your Federal refund?

I don't know the significance of your email, but I can tell you how to check on your refund and whether the intermediary bank has received it and subtracted fees or not.

First, be sure the IRS has actually released your refund.  You can check with the IRS "Where's My Refund" tool:

https://www.irs.gov/Refunds

If that IRS tool shows that the refund has been sent, here's how you can check on it at the level of the intermediary company (SBTPG) that handles that process when fees are paid out of the Federal refund.

To log in at SBTPG's website, choose the taxpayer portal at:
https://www.sbtpg.com/

SBTPG has a phone contact page at the following link. It also shows their business hours.  Even when they are closed, you may be able to get automated info, or you can log in as above.

https://help.sbtpg.com/hc/en-us/articles/230084587-Contact-Information