I say, and with God's help: In truth, wearing it is better and more modest for her, and further away from temptation, but wearing it is not obligatory; because the face is not considered 'awrah (nakedness). Therefore, the benefit should be assessed by the family regarding wearing it. If the benefit is in wearing it, she should wear it, otherwise, she should not. Based on that, one should talk to the girl, and if she insists on it, they should leave the choice to her in that matter, and God knows best.