I think they suspect that she is not ill or wheel chair bound that its just a ploy to gain the dukes sympethies. And that they have been paying off the doctor to lie for them
Pretty sure they are lying about the illness and they were taking money from the duke dude. There was a whole spoiler I read before, but I’m not sure where to find it
'You can only stay under one condition: that you allow me to pay for better medical treatment!!!! Mwahahahaha!!!!'
'You MONSTER!'