Yeah... Kaguya has definitely dragged Mokō back to Eientei before, at least to have Eirin check her out. Or maybe Eirin herself was the one who got to Mokō one way or another to confirm that the girl really is a Hōraian (or Hōrainese? What would be a good word for this? 🤔).

And I kinda recall in FDS, it really felt like Mokō has been in-and-out of Eientei too? Like, not a regular, but definitely not just occasional.