I was a trained nanny and we were told (in those dim, dark days) that little children absorbs everything and negative phrases such as 'silly girl' were totally unacceptable.
As a mother, I feel the same way.
In fact I made a BIG mistake with my son when Dad's Army was on TV. Mainwairing used to say 'stupid boy!' to Sgt Pike and I used the same expression (with the same bombastic voice, so it was partially a joke) but it wasn't to my son.
One day he said, quite calmly, 'Actually Mum, I'm not stupid.'
It pierced me to the heart because I hadn't realised the impact of that throw-away phrase.
My boy was, by anyone's estimation, a very intelligent person - who sometimes did daft things, as we all do.
So never, ever underestimate what you are doing to a child's fragile psyche with expresson such as this.
If this Nanny is as nice as you say, she's not going to up and leave because the people who are paying her , ask her not to tell their little daughter she is silly, when she is NOT.