Does a Muslim woman need to cover her entire body (including hands and face) during prayer if a non-mahram man can see her?

Islam Q&A quote the Standing Committee for Issuing Fatwas, who write: > A woman is required to cover all of her body when praying, except the face and hands, but **if she is praying where there are non-mahram men who can see her, then she has to cover all of her body including the face and hands.** I'm a bit surprised by this: it implies the moment she stops praying she can reveal her hands and face to the exact same non-mahram men she is required to conceal them from during prayer. **Question**: Does a Muslim woman need to cover her entire body (including hands and face) during prayer if a non-mahram can see her? Basically, I want to check if the specific claim in this fatwa is held true throughout Islam, or if it among the more conservative viewpoints. ---- *Motivation*: At work, I found an infrequently used room and put a rug1 in it for prayer and occasionally people see me pray (both men and women; non-mahram; usually non-Muslim). When covering my face, I feel claustrophobic and struggle to breathe. 1I chose one that doesn't look like a prayer rug so as to not overwhelm people (see https://islam.stackexchange.com/q/34782/17163) .