Has it been established that they in fact do? Like I mentioned earlier, there was a court ruling that specifically stated "Rorion "do[es] not have a valid service mark for the name GRACIE JIUJITSU" As I'm neither a lawyer nor have I seen any later details of cases, I'm not sure if that's still true, but would appear that Rorion has been successfully challenged over trademarking GJJ and lost.
Originally Posted by TEA
Either way, I don't think it matters all that much. To quote myself from the long post on BJJ history:
Carlson Gracie, in a typically forthright interview in 1997 with O Tatame, stated that "My Jiu-Jitsu is completely different from theirs, my technique has nothing to do with "Gracie Jiu-Jitsu". I AM CARLSON GRACIE and that's the way it is in the ring."  Kid Peligro, in a Fightworks Podcast interview, offers a different perspective:
To me, its always been just 'jiu-jitsu', because there is not a distinction in Brazil. I grew up just knowing it as 'jiu jitsu' [...] To me its Gracie jiu jitsu and Brazilian jiu jitsu: its all the same thing. We sweep, we choke and we get choked. I say it both ways, it doesn't matter.
Rickson would seem to agree, responding to the question of what he calls his style by saying simply, "I'm Rickson Gracie, I practice jujutsu, and I'm from Brazil. You can think whatever you want. Heh, heh, heh. I'm not too much into names."