"You don't plop the flat end of P.E.T.E. (or button) between your lips and teeth and forcibly pull it out without bruising your lips, what you do is use the lip and facial muscles to resist the removal against and increasing pull force.
YES!! What I do is to pull the button out slowly while gripping my corner closed on the string and once I get the corner of the lip out to a certain point (without causing pain) I pull the button back with my corners and repeat this. Like Ed said, it's a resistance exercise.