In the scene with the martian girl in the middle of the movie, she follows Jerry the press secretary into the White House where she gets a piece of her face ripped away. Then she bites Jerry's finger off, exposing the martian mouth underneath. When the Martian girl kills Jerry with a statue she then takes a piece of gum out of her purse. When she opens her mouth to put the new piece of gum in, you can clearly see that the martian mouth does not open along with hers. It is very clear that the martian mouth is just something stuck on the side of her face.