The iconic scarf straightening scene near the start of the Maria-sama ga Miteru (aka Marimite; or in English: The Virgin Mary is Watching You) Japanese light novel by Konno Yukiko (今野 由紀子), published between 1998 and 2012, with TV anime series & OVA by Studio Deen which aired between 2004 and 2009.
It's a scene that's often been referenced or parodied in many other anime (Lucky Star, Seitokai Yakuindomo, Haiyore! Nyaruko-san, among others).
Basically, the most revered student of a certain elite girl's school, 2nd year Sachiko Ogasawara (小笠原 祥子) abruptly stops and straightens Yumi Fukuzawa's (福沢 祐巳) sailor suit tie (technically called a neckerchief) a new 1st year student. Yumi is one of Sachiko's many fans and this embarrassing incident for Yumi becomes the first link in a chain of events concerning Yumi (the protagonist of the story) with Sachiko and the rest of the elite, all-girls' Catholic school's esteemed (and revered) Student Council members.
Note: I couldn't resist opening with a close-up of those triple-folded white socks with ballet-style black leather shoes which form part of that super classy school uniform. Undisputedly one of the classiest anime sailor-fuku ever:
i.imgur.com/Ear1DtP.jpg
Gokigenyou! (ごきげんよう!)