That is so funny....because my cat gets them under the door too. I live in an apartment building, and I find them in the hallway when I am leaving in the morning or coming home. Once the cleaning lady, who vaccumes the halls etc, said to me...oh I have something for you...she went into her pocket and handed me 3 milk jug rings. We both laughed. I thought it was rather sweet for her to save them and give them back to me.
Jazz sticks his paw under the door all the time. He meows and meows if I'm in the hallway talking to someone and he can hear me. Cats rule