Well now. I'm gonna put my money on secret black-ops operations disappearing critically injured soldiers and turning them into bio-engineered weapons.
The word used for "special(-duty)" in the original Japanese (特務) does have that connotation, yes. Spies, black-ops, secret tech, cloak-and-dagger stuff. Couldn't really think of a suitable English equivalent right now, but how the word "Special" is used in British military* stuff does come close.
Another thing to note... that track jacket worn by the Lieutenant on the previous page? And the one worn by another member of Banshee Squad all the way back here? Yep, all the same pattern, same as the one being worn by Kuchisake-onna. Foreshadowing, ahoy!
