In which rituals must the woman performing 'Umrah and the woman performing Hajj be in a state of wudu' and purity?

Purity is obligatory only for the circumambulation (Tawaf), based on the Prophet's (peace be upon him) saying: "Circumambulation (Tawaf) is prayer, except that Allah has permitted speech in it. So do not speak in it except for good." And based on his (peace be upon him) saying to 'Aisha when she menstruated: "Do what a pilgrim does, except that you do not circumambulate the House until you become pure."