You know it's really annoying hearing that their illegitimate children because technically they're not
true but calling a child illegitimate as an insult instead of describing their origin, is too much for a child. There's a lot of children born from their parents' mistakes.(like born from adulterous relationship), but they became traumatic and unstable since everyone who knows them calling them as illegitimate like they're insulting them for being born that way) insulting them like that will be planted in these children's mind and eventually, they will exclude themselves(some children will think that they're unworthy of love since people calling them illegitimate as an insult and that is a biggest impact of the life of a child).
Since they're starting to let women work at the palace they need to keep an eye on them