Man, I decided to do just that, and it was almost exactly what I thought (minus the technical words): if a velociraptor can do a metric fuckle of damage with their two hook-toes, a T-Rex with 2 of those on each hand can fuck something up, presuming it's close enough (which, as the T-Rex head/bite-force, and distance from the jaw suggests), would have been pretty frequently.

Even if each claw only did a little damage, that's still a lot of blood loss throughout the conflict, and the T-Rex would be more likely to win.