Women is allowed to take attend classes of Qur'an or Tajweed during her menstrual cycle but she must abide by the following rules during such sessions:
1- She should not touch the Qur'an with bare hands. Likewise, she should refrain from touching the Qur'anic text on ipad or digital screen unless it is through a stylus.
2- She should not recite the Qur'an during this period. She may practice her Tajweed by way of breaking the Verse into words and not read the portion or whole Verse all at once.
3- She may touch the Tafseer book, if it is determined that the words of Tafseer exceed the words of Qur'an. It would still be preferred to avoid touching the Tafseer book with bare hands during this time.
Islam does not prohibit a woman from continuing the remembrance of Allah during her menstrual cycle. There are a few things that she is not allowed to do during this time and among those things are: 1) entering the Masjid 2) reciting the Qur'an, 3) touching the Qur'an, 4) performing the Tawaf
And Allah knows best.
Mufti Ikram ul Haq
Fatwa Center of America