of course I would trt - and like 237SJ, I had to cover when I went to Saudi Arabia. ALL women have to cover there, it's the law for Muslims and non-Muslims, but it's up to you whether you just wear normal hijab (long coverall and headscarf is most appropriate) or wear the burka or niqab which actually cover your face. Many residents wore niqab so kept their eyes on view, but others covered completely when out of the house. It's the norm - the women I met just did it without thinking about it, a bit like we put on our raincoat to go out. Women are wearing ordinary clothes under the outer covering, some had very posh clothes and beautiful hairdos too.
It makes no odds to me whether I can see the whole face of the person I am giving the money to - it's another woman, not a Martian. Where however there is a question of security (and as we have discussed many times before, in a bank or at the airport) then the face should be shown.