Personally, I believe that Car Gurus needs to work on holding their dealers accountable rather than work arounds that won't work.
Car Dealers have done a really good job of "gaming the system" with Car Gurus. It all started with the slimy pricing strategy where the price is 15,000 but to get that price you have to buy the (name the product or condition here) whatever. That gave those dealerships a tremendous advantage.
Now many dealers are simply leaving their vehicles on the 3rd Party Marketplaces after they are sold. It isn't accidental. They know that the more vehicles they have listed, the more action they will get.
So implementing this Text Message strategy won't help them because these dealerships will just reply "Yes" without even looking. Everyone in the store will be trained to handle this. No matter what the response will be "I'm sorry, that car was literally just sold. Customer had been looking at it if 2 days and just blew in and got it".
Car Gurus is likely getting frequent shopper feedback about getting to the dealership and the vehicle being sold.