What is the ruling on a menstruating woman or someone in a state of major ritual impurity (junub) reciting the morning and evening remembrances (adhkar)?

There is no harm in a menstruating woman or someone in a state of janabah (major ritual impurity) reciting adhkar (remembrances of Allah). The preponderant opinion is that it is permissible for a menstruating woman to recite the Quran without touching the mushaf (physical copy of the Quran).