Desperate to be a hero, Tom stops the would-be assassin, and then chases her as she runs away.
In the middle of their breakneck chase, Tom wonders "if [the assassin] was pretty: a beautiful assassin from the Anti-Traction League" (3.4). Dude, pay attention. What are you thinking with here? Your head or your... um, heart?
After a long pursuit, Tom corners the assassin near the waste chute. To answer his previous question: she ain't pretty. She has a long scar across her face and only one eye.
"Ask [Valentine] what he did to Hester Shaw!" (3.14) she shouts, and down the poop chute she goes.
Valentine finally catches up. He asks Tom if she had a scar, and Tom says yes.
Valentine puts a hand on Tom's shoulder. Tom thinks it's to comfort him, but then BAM, Valentine shoves Tom down the waste chute too, plunging him into deep darkness.