The box of snack sticks that Karen Onodera and Marie eats are called Prech. It is a fictional clone of Pretz, a pretzel-styled biscuit stick snack manufactured in Japan. This is a continuation of the joke from Onegai Teacher, which had Mizuho's snacks being Pochy, a fictional clone to Pocky. Because of trademark infringement, it is common for anime writers to change the names of popular brand names, thereby circumventing the legal dilemma of using real world brand names.
When Karen and Miina go for the interview at the school, the names they come up with are Kikuko Inoue and Yayoi Inoue. Kikuko Inoue is the Japanese voice for Miss Kazami in Teacher/Twins (also Belldandy in A!MG and many more series). Yayoi Inoue is the name of Kikuko's sister
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