Good on her. I think the appropriate response from her should be "its cute that you think I should do that."
When we were there, women were not required to wear head scarves. The only accommodation our military women made was that they were allowed to wear their hats indoors if they chose to. This had an impact in bartering and haggling over purchase prices. Not much else. Even those that chose to wear a head scarf where seen with disrespect. I understan for a time later that the military had all the women covering their heads. Dont know if that is still the practice.