Should a deserted mosque that has become a Quran memorization center be treated as a mosque or a memorization center in terms of a menstruating woman entering it and performing the two-rak'ah greeting prayer upon entering a mosque?

The basic principle is that it is not permissible to convert mosques from the purpose for which they were built. They are an endowment for Allah Almighty, and it is not permissible to revoke them or demolish them. This is the view of the majority of scholars. However, if a valid interest necessitates changing the mosque—such as its abandonment and the cessation of its benefits—then there is no objection to that. Accordingly, there is no objection to using an abandoned mosque as a house for memorizing the Holy Qur'an, and it will no longer have the rulings of a mosque concerning ritual impurity (janabah), menstruation (hayd), post-natal bleeding (nifas), greeting the mosque (tahiyyat al-masjid), and other related matters.