A few days from now, a week at most, Carter would be in the system, and all evidence that he’d ever existed would be wiped from the face of the earth. Even the warden would swear he’d never heard of the guy.
-- Narrator (Chapter 3)

Importance: Wolgast and Doyle are sent to Terrell to talk Carter into taking part in Project NOAH. Wolgast knows how quickly things will be set in motion in regard to making Carter disappear if he agrees to participate in the experiment.

So, let’s say the same GI takes the same piece of shrapnel but within half a day his body’s healed itself and he’s back in his unit, fighting for God and country. You think the military wouldn’t be interested in something like that?
-- Sykes (Chapter 3)

Importance: Sykes explains to Wolgast why Project NOAH is such a big asset for the military. Instead of losing money...