Elijah knew "a force" was at work to keep heroes and villains hidden, that's it. He didn't know details, let along a name (M. Night himself said he didn't give the society a name), just that "a force" existed and that he had to work around them to get heroes and villains exposed. How? He's a super genius that can calculate odds and variables. Certain things would and would not happen if a third, unknown party wasn't pulling the strings. Simple deduction on his part.

Now I'd call foul if he did know the name and that Staple was a member...but he did not. Just that someone or something is working against him.

I think the recurrence of shamrock tattoos on people's wrist might have been a clue to some form of social connection. The idea that millions were being spent on weird treatments of 3 mass murderers might also have been a clue that this wasn't an ordinary incarceration.

What is it with secret organisations in fiction and all these clearly obvious signifiers of an individual's membership? Sorta undoes the 'secret' part.