[Hooves]

What we can conclude from episode 4 is that Shuu is now doubting Gai and his motives against GHQ. Which might lead him to use the tracker or not (or was it something else?), after the initial episode 1-2 battle, it sorta gave Shuu a bad viewpoint of GHQ. But after episode 4, this viewpoint was altered by Gai wanting to free a mass murderer. He might even feel left out that he was not being saved (well he was going to be freed anyway but in a subtle way) it still could bring down some trust.

But it's clearly decided that Shuu will take the side of Funeral Parlor since GHQ will simply "throw the trash away once used". Now if GHQ is not a backstabbing organization, they can express their good will on Shuu to give him a better light when looking in that direction instead of "Oh look I got what I want, now you can go die".