Matter, Eaten: Give Matter-Eater Lad a free action and destroy an adjacent wall, adjacent square of blocking terrain, or remove an object in his square or an adjacent square from the game.

Can Matter-Eater Lad remove an object that is held by a character?
No. He can only remove objects that are in an adjacent square or his square.

Can Matter-Eater Lad remove the Crimson Gem of Cyttorak or other objects that can't be destroyed?
Yes. He removes objects. That is not the same thing as destroying them.

What if a character has already put the Crimson Gem (or whatever) on their character card?
No. As mentioned above, he can only remove objects that are in an adjacent square or in his square.