I am asking this question on behalf of a Muslim sister. She performed Hajj two times while covering her face. She did so because she was uncomfortable in the presence of men when she was outside. She did this knowing that it's prohibited to cover her face during Hajj. She is now worried and wants to know if there is any compensation needed for this?

Covering the face during the Hajj for women is allowed. What is not allowed is the Niqab, that piece of cloth that has two openings for the eyes, that is Haram. But if she was drawing down the veil itself as Ayesha used to do over her face, so her Hajj is correct.

But if she was wearing Niqab, the one with the openings for the eyes during the Hajj and gloves, then in this case she committed what we call something of Mahdthurat Al-Ihram “things that a Muhrim or the pilgrim should not do”, and of course she has to expiate for the Hajj, and the expiation is to slaughter a goat in Makkah. Sending the money to anyone who is there to slaughter a sheep or goat in Makkah.