Saying La Ilaha Illallah during a woman’s period is okay. Interestingly, it is mustahabb for a women on their period to clean themselves of blood and change their cloth or cotton and make wudu and if not possible, to do tayammum and sit where they usually pray and engage in supplication and dua and dhikr and salawat.
 Tawdihul-Masa’el (annotated by Imam Khomeini), vol. 1, pg. 269.
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