Catholic scarf (?) (Boston)

I know this might be a weird request. But I’ve noticed that many of the women at my husband’s place of worship have their hair covered with some sort of lacy scarf. I am not Catholic but my husband is. He almost died recently and I want to go with him and show the upmost respect and gratitude I can towards his God.

So I was wondering does anyone have an older one they no longer need or want that I can have? And any advice on customs or taboos would be very appreciated. Thank you.