Before you get too concerned about theft, be aware there are at least 3 legitimate reasons that a refund would go to routing and account numbers you don't recognize. I will tell you some possibilities below.
First, look at your return at a page called "Electronic Filing Instructions" or a page called "Federal Tax Return Summary." Those pages will have the account and routing numbers, but also may tell you additional information and the refund option selected.
The name of the bank is likely going to be your biggest clue.
For instance, you mentioned the bank is in Texas, so I wonder if it is MVB Bank by any chance? MVB Bank is used when a filer chooses to get their refund on a Credit Karma Money checking or savings account and the Credit Karma Visa Debit Card. Did you choose that option and don't remember doing so? Here's info on it:
https://sh-exp-ck.app.intuit.com/s/en-us/help-article/chequing-account/getting-know-credit-karma-mon...
Another possibility is if you chose to pay any fees out of your Federal refund. In that case the refund would go from the IRS to an intermediary bank where the fees are taken out. Then that intermediary bank sends the rest of the funds on to your own bank account. But I don't think that service uses a Texas bank.
Did you pay the fees upfront, or did you choose to pay them out of your Federal refund? If so, we can tell you how to check with the third-party company that handles that.
Thirdly, occasionally someone who has a brokerage account will see TurboTax send their refund to their brokerage account unknowingly, especially if the user had used the import feature from their brokerage. We have seen this happen to a few users who said their refund went to a JP Morgan or Chase bank account they didn't recognize.
