Indeed that was the case:

According to The Strange History of Taco Tuesday, the promotional phrase was started in 1982 by a chain called Taco John’s based out of Cheyenne, Wyoming. In fact, Taco John’s placed a registered trademark on the phrase in 1989 to attach it to their brand. They filed a lawsuit against another restaurant chain after seeing that it was used, but the lawsuit resulted in bad press, so they have stopped enforcing their trademark. They still use it as their brand’s signature, and rightfully so!

https://bennystacos.com/taco-tuesday-legendary-tradition/

So Taco John gave up the trademark and now any restaurant can advertise "Taco Tuesday" specials.