Yeah, I used to be at a barn where people, including instructors, were very lax about sweeping the aisle, picking poo from the arena, or putting away jumps when not in use, and it drove me a bit nuts because I had grown up assuming that was the "etiquette" at all barns (though overall that barn was great, particularly the horse care). And to be really honest, since no one else seemed to bother cleaning up, I started wondering why I was taking the time and got a little lazy about it.
I moved to a barn where the etiquette is very clear and all the boarders take it very seriously. When I got my first tour from the BO, she went through the barn rules, and mentioned that a former
boarder behaved like the young lady you're describing and she was asked to leave- the other boarders cared so much about the rules they couldn't tolerate the bad behavior and the BO was more interested in keeping her 20 long-term, respectful boarders happy than constantly having to remind someone who couldn't be bothered to take care of their own mess. If your new boarder doesn't seem to get that you take this seriously after your text, then you may have to ask her to leave.
I don't think I'd attribute the behavior solely to being young- I know plenty of very responsible, conscientious young horsepeople who would never act that way (there is a 15 year old at my current barn who leaves the area pristine after working with her two horses). Sounds like this is a personal issue with appreciating the rules of your barn.
For the record, I easily got back with the cleanup program as soon as I was back in an environment where people cared about it