The majority of scholars agree that ritual purity (taharah) is not a condition for the validity of سعی between Safa and Marwa. This is because سعی is not performed inside the مسجد الحرام itself, and نبی کریم (صلی اللہ علیہ وسلم) told Aisha to do everything that a حاجی does except طواف around the کعبۃ اللہ. Since سعی was not excluded, it indicates that purity is not required for it.
Sheikh Ibn Baz confirmed that سعی is valid without وضو and without غسل, stating that purity is مستحب (mustahabb) but not required for سعی. However, he clarified an important practical point: since سعی must come after a valid طواف, and طواف requires purity, a menstruating woman should first wait until she is pure, perform غسل, do her طواف, and then perform سعی. She cannot perform سعی before doing her طواف.
Sheikh Ibn Uthaymeen added that in the case of حج, if a woman has already performed طواف al-Qudum before her menses began and has not yet done سعی, she may perform سعی even while menstruating, since it follows a valid طواف. The key distinction is that سعی itself does not require purity, but its prerequisite — طواف — does.