The last words of the father were the highlights of the chapter for me. What a bad timing to laugh, but man, this author has no mercy, even for poor Mei.
She was referencing Class S tropes from a specific type of relationship between girls in the early 20th century. This is a very old but popular moe cliché, so it's often parodied in the media as inexperienced characters expect it to be normal practice in girls' schools to this day.