I feel like she became her personal maid to avoid whatever misfortune it is that always happen to the villainess and obviously to watch claire's sleepy face in the morning
If this story wasn't so comedic in nature, Rei's behavior is downright pushy, stalker-ish and very annoying to Claire that would be enough to get a restraining order against her...
@ravidya I'm guessing it was a type of blackmail, but one through knowledge rather than intrigue.
I'm guessing she is actually very versed in the finances of the Kingdom and knows which nobles are misusing the allocated funds, so she just stated one of the highest hitters on that list.
Though, as I said, that's what I'm guessing.
It could also be a blackmail for knowing things given to or given by someone as "finances" for a "investment"