Praise be to Allah.
Al-Bukhaari (314) and Muslim (332) narrated from ‘Aa’ishah (may Allah be pleased with her) that Asma’ asked the Prophet (peace and blessings of Allah be upon him) about ghusl following menses. He said: “Let one of you take her water and lotus leaves and clean herself well, then let her pour water over her head and rub it vigorously so that it will reach the roots of her hair. Then let her pour the water over herself, then take a piece of cloth scented with musk and purify herself.” Asma’ said: How should she purify herself? He said: “Subhaan-Allah! Purify yourself with it.” ‘Aa’ishah said – as if she whispered it to her – Follow the traces of blood.
The reason for using this is to perfume the site and ward off unpleasant odours.
Al-Nawawi (may Allah have mercy on him) said in Sharh Muslim: The scholars differed concerning the reason for using musk. The correct view is that of the majority of our companions and others, which is that the purpose of using musk is to perfume the site and ward off unpleasant odours. … She should use it after ghusl. If no musk is available, she should use whatever perfume she can find. If she cannot find any perfume then it is mustahabb for her to use whatever will remove the odour [soap, nowadays]. If she cannot find anything, then water is sufficient for her, but if she fails to perfume it when perfume is available, that is makrooh. If she is not able to do it then it is not makrooh in her case. End quote.
Dr. Aaminah ‘Ali Naasir Siddeeq, professor of microbiology in the College of Science in Jeddah has discovered that musk is a natural antibiotic for treating skin diseases and genital diseases in humans and animals. This discovery was patented in the King ‘Abd al-‘Azeez City for Science and Technology in Riyadh.
The researcher also presented to the Eighth International Conference on scientific miracles in the Qur'aan and Sunnah, held in Kuwait in 1427 AH a paper entitled: Aspects of the scientific miracles of using musk as an antibiotic against funguses and yeasts that cause disease in humans, animals and plants..
She explained that disease-causing bacteria increase in number during the menstrual period and that musk has a strong effect in killing off these harmful microbes.
It is clear that the reason for the menstruating woman using musk is to perfume the site, to ward off unpleasant odours, and to kill off disease-causing funguses and yeasts.
And Allah knows best.