The majority of scholars agree that ritual purity (taharah) is not a condition for the validity of Say between Safa and Marwa. This is because Say is not performed inside the Mescid-i Haram itself, and Hz. Peygamber (sallallahu aleyhi ve sellem) told Aisha to do everything that a haci does except Tavaf around the Kabe. Since Say was not excluded, it indicates that purity is not required for it.
Sheikh Ibn Baz confirmed that Say is valid without abdest and without gusul, stating that purity is sunnet (mustahabb) but not required for Say. However, he clarified an important practical point: since Say must come after a valid Tavaf, and Tavaf requires purity, a menstruating woman should first wait until she is pure, perform gusul, do her Tavaf, and then perform Say. She cannot perform Say before doing her Tavaf.
Sheikh Ibn Uthaymeen added that in the case of Hac, if a woman has already performed Tavaf al-Qudum before her menses began and has not yet done Say, she may perform Say even while menstruating, since it follows a valid Tavaf. The key distinction is that Say itself does not require purity, but its prerequisite — Tavaf — does.