Very true, but their goal is more layered. It attacks Will's credibility, yes. But it also attacks Will's mental health as Lisa pointed out a few chapters back. The order seek to topple the Prime Minister, push Will (via Caleb's support) then destabalize him through a multipronged attack on his sensibilities, his image, and his mental stability. Making sure to prime everything for an election. They need to remove Will from play, otherwise their Bob Hesston move is simply not going to work. And Will, for all his faults, is a deeply popular politician, entrenched, and that makes removing him really difficult for Abernathy.
Sorry I like thinking this through, it helps me formulate the story and focus in on their motivations. I try to keep these thoughts strictly spoiler free, merely focused on the narrative to the point of commenting. I know what happens, true, but I like putting myself into the mind of a reader as well. It lets me feel the story out a bit better.