All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
May Allaah reward you for your enthusiasm for the Hijab and your chastity. We ask Allaah, The Almighty, to increase your zeal for doing good.
A Muslim woman is ordained in Islam to observe Hijab in front of non-Mahram men, and it is not permissible for her to remove it in the presence of a non-Mahram man.
However, it is permissible for her to take off her Hijab in the presence of women and show what is permissible to show in front of them. We have already explained in Fatwa 84062 the ‘Awrah of a Muslim woman in front of other Muslim sisters, and if she wears a scarf or puts something on her head for the sake of decency and respect or Hayaa' (modesty and shyness) of showing the hair, then there is nothing wrong in this, as all Hayaa' is good.
It should be noted that in case she believes that a non-Mahram man has most likely entered her place, then she is obliged to observe the Hijab.
Allaah Knows best.