The woman must be convinced that head-covering is a religious obligation which is decreed by Allah and his Prophet Muhammad and agreed in consensus by the entire Muslim Community. Allah decreed this modesty upon the Muslim woman so that she is easily distinguished from the non-Muslim and from the non-obedient. Her mere clothing gives a clear signal that she is a serious and obedient woman, which deters all those that may have illness in their hearts.
We must also help the sister by placing her within a good company of Muslim sisters, so that she may follow them and be helped by them. It is essential that we treat the sister in a lenient and gentle manner, rather than in a strict and rough way, as Allah always loves and blesses leniency and gentleness.
Despite the head cover (or Hijab, as is called today), being an obligation upon all Muslim sisters, it remains a secondary branch of religion. Therefore, if being strict in this matter will ultimately lead to the sister turning back on the major principles of Islam, or indeed, Islam entirely, it is extremely unwise to make a person leave a basic principle and a pillar of religion for the sake of a secondary matter, never mind leaving the religion in its entirety.The Fiqh of balances forces us, at times, to overlook this wrong-doing (Munkar) so that a greater sin is averted. This is a well-known and approved principle.
However, whilst we overlook this matter at this moment of time, we must not give up on this sister returning to the straight path and the correct way, praying for Allah to give her guidance and treating her in a beautiful and gentle manner. It remains that despite this being an undeniable haram (forbidden offense), it remains a minor, not a major sin. Minor sins remain matters which could be overlooked whilst major sins (Kaba'ir) could never be overlooked and disregarded.