If only they didn't try to starve the poor creature, never giving it even a modicum of food, any kitty treats, nor tube... at least not in living memory...

They're actually rearranging the letters to say

"No I won't; feed me."

Is there glue on the back of the letters, perhaps under whatever covering they have to stick on the board?

Because many cats are glue fiends. An old one I used to know would eat tape, books of stamps, all sorts of stuff. IDK why.