SPOILERS(Probably)
Basically, what happens is Gyaru pursues Mei about her "inside depression" (I can't phrase it any better) and Mei, of course, being the tsundere that she is, unleashes her tsuns and gets defensive when Gyaru goes to her and says "It's okay! I'm here for you!" etc.etc.
Dad gets pissed, and threatens her that if she protects Mei, she's gon' get expelled.
Gyaru meets with Gyarufriend and talks about the expulsion and how she's a bad sister, blablabla, but then Gyarufriend manages to encourage her and says "No, I think you're working really hard as a big sister, and the little sister should be really happy." which leads to Gyaru to decide that she'll not 'run away' anymore.
You should know what happens next.
The nurse says to Mei, "There was this girl who ran around crazily helped the old man, explained the situation to us thoroughly, helped him to the ambulance car and stuff. She wanted to let the grandchild (Mei) know." Mei, of course, shows her surprised face, slowly revealing the dere.
And so Mei and Gyaru have a nice 'sisterly' bond with one another, and Mei tells her "Call me by my name. Isn't that what families do?"
Gyaru then goes to the station, giddy, happy that she's friendlier with her sister now. She stands there before the door and thinks "So... we're sisters..."
Bam. Cliffrigginhanger.
Hope this didn't feel to long and helped you. Also, no Het so far, besides the fact that the teacher Mei's engaged to is a total douchewad