I won't put any spoilers here but I don't understand what the mission is saying.

In essence, I have just killed a special character and the instruction is,

" Turn each card depleted by this figure's Insider Information ability faceup. They can be used normally."

To quote Ozymandias, "nothing beside remains"... I have no idea what that instruction is referring to.

Please help.

Probably the Insider Information ability has not yet done anything, so there are no cards to turn faceup.

Possibly. It may have applied if I hadn't killed the end-of-level boss in one very lucky move. Will see how it goes when I run the campaign with friends this evening.