This seems fishy. Why would they want to lose to jean on purpose? That isnt to her benefit, that would only inflate her ego and prevent her from maximizing her skills for combat...
@eng1 They might mean it in as in he loses to her requests. So instead of fighting her on her "brattiness" just give into her requests and do as she wants.
If they do mean it as legitimate "just let Jeanie win all her battles," it might be because they don't want her to give up on her spirit studies. She's clearly someone who has the most potential for furthering the research on spirits, so it might be better to give her a big ego if they can at least study her interactions with the spirits and see what she finds out about them (even if they don't know she has 3 already).
She deadly and badass. I don't think that she will be fooled to thinking she's strong & get complacent by these high ranking ppl. Especially seeing how much of an effect the mercenaries had on her with that one quote: "Get Stronger" or something like that. She's obviously not going to be satisfied with this little academy. (Hopefully that's just my prediction)