Jake shoos the cat away from Lenny's supper and then pushes the chair up to the table. A minute later, when Lenny comes out of her room, the chair is pushed out again, even though Jake's hands have been occupied the whole time.
Jake sees Lenny studying his Purple Heart and tells her to stop. He has to move the doorway curtain out of the way. Since the curtain covered the room with no gaps, there is no way he could have seen what she was doing.