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If the person who is doing tamattu‘ exits ihram following his ‘umrah, then the time for Hajj comes, he should enter ihram for it. Ihram is the intention to do the rituals, and the place for the intention is the heart; it is neither stipulated nor recommended to utter it, nor is it stipulated to do ghusl and clean oneself, although it is preferable to do ghusl when entering ihram.
A woman may enter ihram in her ordinary clothing; she does not have to wear any specific garments.
If what you mean is that she did not do ghusl or utter the intention or recite the talbiyah, or she did not put on a special garment, then that does not matter.
The fact that she went out with the people to Mina, then to ‘Arafah, and she did the rituals, and refrained from doing the things that are prohibited, all of that indicates that the intention to do Hajj was present.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: A woman does not know the three ways of doing Hajj, and she does not know the intention for that. She has done Hajj five times, and she does Hajj on the day of at-Tarwiyah (the eighth of Dhu’l-Hijjah). She goes with the people, when they go to ‘Arafah and to Muzdalifah, and she stones the Jamaraat. She does not have a specific intention for any of the three ways of doing Hajj. Is her Hajj during these years valid?
He replied:
What appears to be the case is that her Hajj is valid, because it is as if she is saying: I am entering ihram for whatever the people have entered ihram for, and entering ihram for whatever someone else entered ihram for is permissible, as the Prophet (blessings and peace of Allah be upon him) said to ‘Ali ibn Abi Taalib during the Farewell Pilgrimage, when he had come from Yemen with Abu Moosa al-Ash‘ari (may Allah be pleased with them both). He said to him: “For what have you entered ihram?” He said: For whatever the Messenger of Allah (blessings and peace of Allah be upon him) has entered ihram for. Then he said: I have the hadiy (sacrificial animal) with me. So he made it qiraan (‘umrah followed by Hajj without exiting ihram in between). As for Abu Moosa al-Ash‘ari, he said that he had entered ihram for what the Messenger of Allah (blessings and peace of Allah be upon him) had entered ihram for, but he did not have a sacrificial animal with him, so he instructed him to make it ‘umrah, because tamattu‘ is better than qiraan.
It seems to us that this woman undoubtedly entered ihram for whatever the people entered ihram for, and that she said: I will do whatever the people do. But when a person wants to do an act of worship, whether it is Hajj, fasting, giving charity, or anything else, he must learn before he goes ahead and does it. But if after doing it he comes and asks: what is the ruling? This is undoubtedly not the best approach.
End quote from Majmoo‘ Fataawa Ibn ‘Uthaymeen (22/22)
What appears to be the case is that the Hajj of this woman is valid, and she does not have to do anything.
And Allah knows best.