Precocious cheeky behaviour in six year old grandaughter

The child I mentioned was referred to as Shirley Temple because she was always showing off, singing songs, doing dance routines, butting into adult conversations and attempting to dominate any gathering, children or adult. In fact, behaving like the roles Shirley Temple played on screen. It was her aunt who told me the family nickname, and she went on to give a great deal of support to this girl when her parents collapsed.
I am well aware of Shirley Temple's background, her childhood exploitation , and how she later achieved status as a diplomat. But her film persona was obnoxious.
Different ways of viewing children: it is the quiet polite children who go on to achieve and the bright outgoing children who cannot understand why nobody finds them wonderful when their childish cuteness disappears, boys as well as girls. I could give you other examples of precocious children coming to grief in their teens because they were so indulged by their parents.
I think the grandmother is absolutely right to be concerned.

Different ways of viewing children: it is the quiet polite children who go on to achieve and the bright outgoing children who cannot understand why nobody finds them wonderful when their childish cuteness disappears, boys as well as girls.

And here was me thinking that bright, outgoing, children were likely to be our next leaders, actors, pop stars, etc.
Instead of quashing the child, maybe channelling their energies might be a better way forward. There are so many girls in the classroom who don't have the courage of their convictions in front of their peers, I don't understand why anybody would try to quash that.
Doodledog, you put it so much more succinctly than me. Well said!

I guess we don’t know enough about the little girl’s behaviour but I’m wondering about your relationship with her parents.

Would you feel able to tell them that you’re “worried” how your granddaughter might lose friends because of the way she behaves sometimes. If you can find a way to approach this by sounding concerned and supportive rather than critical.

Best of luck and I hope you find a way to enjoy her company