The gymnastics coach character, Ilya Korska, is based on Romanian Bela Karolyi who, through tough love, successfully coached several gymnastics world champions - Nadia Comaneci, Mary Lou Retton, Julianne McNamara, and Kerri Strug.
Pixies, which the episode's title references, are a race of small, winged mythical creatures who represent innocence and magical whimsy. "Pixie" is also an endearing pet name for little girls.