Okay im a muslim myself,and i have heard many incidents like this so ill provide the most logical answer with the Islamic view.
First of all,there are certain things that we need to know before any kind of judgement can be given:
1.Did the girl really suffer from any kind of mental illness?
2.How the pages of the Quran,got to the streets.
Okay,we still dont know if she really has an illness,but if she does then she should be sent to some kind rehabitation facility.If not,.....she screwed!!!
It is a big shock to know that pages from the Holy Quran got on the streets,i live in pakistan so i know the importance of the Quran there.The Quran is not meant as a simple book,which can be read,learned and then thrown away.It has a huge importance.My mom has a copy,which was passed down from her grandmother,but she doesnt consider it special due to its age or cuz of her grandmother,but since its THE HOLY QURAN! Muslims dont buy the quran like some cheap book,which they can buy over and over again.They buy a copy,and give it a lot of care and respect thats the reason the Quran get passed down to the next generation.I dont expect any unbelievers which i saw on this thread ,to understand this(no offence) since its a thing related to faith.
Now back to the topic,...there are three out comes that can come from this(my opinion):
1.If she does not suffer from any kind of illness,and did it intentially then shes dead one way or the other,since if the law lets her go,someone will murder her.So prison(if shes lucky) is the prefered option.
2.If she does suffer from any kind of mental illness,she still wouldnt be set free.She should be sent to prison but her illness should be treated.From my point of view.it should be some kind of rehabitational facility,where her illness should be treated but she would be grounded.This way she would complete her sentance,while getting treatment for her illness at the same time....Shes poor so i doubt she can get any kind of treatment on her own,and she will contiue to make such mistakes.
3.If she some how is set free and forgiven,then her mother should give her a beating so that she doesnt do this in the future.
I dont think she should be executed,but she should be taught a lesson.Since Islam is not a religion of voilence,but its actually of compassion,sympthy and forgiveness.