Yeah, she doesn't seem to consider Mai as a person really. The reason why she goes to greet Mai personally is to confirm if Mai is the real deal. It probably has something to do with Mai being a remix heart, or something to do with the title of the series, Variable Heart.
And I don't think Mai will go missing now. Meifang seems like she wants to keep a low profile for now(telling her men not to do anything towards the daughter of Yayoi family due to not wanting to deal with them right now).
It's either going to be resolved, or put on hold until after graduation. Or maybe some moves will be made against Mai during her time left in school, but she is able to keep it a secret from the trio.