I really don't have a clue from OP how inappropriate the child is, how well she behaves generally, and whether she has responsibilities beyond her years.
I can picture A:
a bright child, interested in the world and learning about it, trying out her own way of doing things, learning that life isn't always perfect and developing the skills to deal with it.
B:
an anxious child who can only cope with her anxieties by directing the adults in her life.
I'd add that I only recognise 2 forms of 'inappropriate' clothing:
1. likely to cause offence to others
2. likely to result in serious discomfort - eg: if a child goes out in the rain inadequately dressed, for a short walk, returning to a warm house, I'd let them learn a lesson. If we're off for a whole day in the mountains, returning to tent, I'd be very firm - but actually I never needed to be, because they knew how important it was!
Also, I think as GPs, I gree with those who say 'don't criticise the parents' BUT if it impacts on you, when you have the care of her, then you need to talk to them about guidelines.
I've got another 'keen'... Ouch!