Answer
(Fatwa: 749/264/TL=1432)
It is absolutely prohibited to recite the Quran while in menstruation whether the Quran is recited by carrying in hands or verbally. A menstruating woman can touch Islamic books, read as well as read out for others. She even can read a wazifa or dua written therein, but she will have to avoid reciting the Quranic verses only. Yes, if the Quranic verses are recited as dua, it is also allowable.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband