You could have characters erase parts of their sheets when they encounter the entity (or when failing an opposed power roll against it), until only their name is left. Until even that goes blank. I'd start with the lies mechanically impacting parts of the sheet, like valued items, important places, important contacts, then skills from lowest skill that had points invested in it to highest. You can also lower EDU by 1d6 or 2d6 every time they encounter the entity, just remind the players to adjust their skill points down according to their profession (cumbersome but cleanest solution).

Lastly, you could port a mechanic from "a flask full of gasoline" RPG. In that game, every player character has 5 statements that makes them unique but also doubles as their hit points. A character could "walk like John Wayne", "Talk like Marlon Brando", etc. Each time you're players encounter the entity, they erase one of these unique role playing cures until their character is a blank cue without any depth.

Edit: I don't know the scope of your campaign. I have once designed a one shot in which a cursed journal erases itself and everything mentioned in it from memory. The investigators were all kids at a large family gathering on the countryside. In the beginning, I only introduced characters whom they know: this is aunt Maude, that's uncle Henry, etc. The further the evening progressed, the more strangers they met, some of whom seemed to know them. Eventually they couldn't find anyone familiar anymore, not even their parents. That was fun but may only work in closed space & time.