Squeaky and Gretchen almost get into a fight. Why, then, do they smile at each other?

At the end of the story Squeaky and Gretchen smile at each other as a sign of mutual respect.  Both girls recognize in each other an opponent worthy of respect. Squeaky realizes that Gretchen is just as serious about running as she is and appreciates this.  It also shows the awakening and growth of Squeaky as a character; up to this point in the story she remains unchanged (flat character).