In actual fact, GZ might have wanted to be a cop.
Indeed, we also now see he wanted to be a prosecutor.
Can't wait for the prosecutor to piss on him for THAT.
But none of that makes TM's brushes with the law (or close brushes with entities akin to the law) relevant to the case. TM is not on trial, being dead.
Again, it would be relevant if he had some tendency towards violence AND IF GZ knew that trait at the time of their unfortunate contact with each other. Beyond that, it has nothing I can see that has anything to do with the trial.