The majority of scholars agree that ritual purity (taharah) is not a condition for the validity of সাঈ between Safa and Marwa. This is because সাঈ is not performed inside the মসজিদুল হারাম itself, and নবী করীম (সাল্লাল্লাহু আলাইহি ওয়া সাল্লাম) told Aisha to do everything that a হাজী does except তাওয়াফ around the কাবা শরীফ. Since সাঈ was not excluded, it indicates that purity is not required for it.
Sheikh Ibn Baz confirmed that সাঈ is valid without অযু and without গোসল, stating that purity is মুস্তাহাব (mustahabb) but not required for সাঈ. However, he clarified an important practical point: since সাঈ must come after a valid তাওয়াফ, and তাওয়াফ requires purity, a menstruating woman should first wait until she is pure, perform গোসল, do her তাওয়াফ, and then perform সাঈ. She cannot perform সাঈ before doing her তাওয়াফ.
Sheikh Ibn Uthaymeen added that in the case of হজ্জ, if a woman has already performed তাওয়াফ al-Qudum before her menses began and has not yet done সাঈ, she may perform সাঈ even while menstruating, since it follows a valid তাওয়াফ. The key distinction is that সাঈ itself does not require purity, but its prerequisite — তাওয়াফ — does.