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.
A woman who is in the state of Ihraam is forbidden to wear Niqaab. This is based on the Hadeeth narrated on the authority of Ibn ‘Umar that he said: "A woman in the state of Ihraam wears neither the Niqaab nor the gloves." [Saheeh]
When a pilgrim woman forgetfully wears the Niqaab, nothing is due on her. Allaah The Exalted Says (what means): {Our Lord, Do not Impose blame upon us if we have forgotten or erred.}[Quran 2: 286] In Hadeeth, it was narrated that in response to this supplication, Allaah The Exalted Says: "I indeed Did it." [Muslim]
As soon as she remembers, she is required to remove the Niqaab as she has become no longer excused.
The Hanbali scholar Ibn Qaasim said: "As soon as one becomes no longer excused due to forgetfulness, ignorance or compulsion, as when he remembers, knows or becomes free of compulsion, he is required to stop what he does of forbidden matters."
If the woman did not remove the Niqaab after remembering the ruling, she is responsible for the compensation. If she could not change it, as mentioned in the question, then she takes the ruling of those who wear form-fitting clothes for need. Consequently, she is required to give the compensation and she is not deemed guilty.
An-Nawawi said: "If the pilgrim needs to cover his head or wear form-fitting clothes due to an excuse such as heat, cold or remedy, or if the woman needs to cover her face, then covering is permissible and the compensation is due. Allaah The Exalted Says (what means): {And whoever among you is ill or has an ailment of the head [making shaving necessary must offer] a compensation.}[Quran 2: 196]"
The compensation is either slaughtering a sheep, feeding six poor persons with half a Saa‘ for each one or fasting three days. A pilgrim chooses one of these options.
The upper piece of cloth which is attached to the Niqaab is of no significance with regards to the ruling on this issue.