Praise be to Allah.
The people who live in Makkah do not have to do the farewell tawaaf, because this tawaaf is required in order to bid farewell to the House, which does not apply in the case of those who live in Makkah, because it is their home. Shaykh al-Islam Ibn Taymiyah said, explaining that the farewell tawaaf is not one of the essential parts of Hajj which must be done:
… Therefore the people who live in Makkah do not have to do tawaaf al-qudoom (tawaaf of arrival) or tawaaf al-wadaa’ (farewell tawaaf), because that does not make sense in their case; they are not coming from elsewhere and they are not bidding farewell so long as they live there.
Majmoo’ al-Fataawa, 26/261
Shaykh Ibn Baaz (may Allaah have mercy on him) said: The people of Makkah do not have to do the farewell tawaaf. Al-Fataawa, 17/393.
This includes everyone who is inside the boundaries of the sanctuary (al-haram). Ibn Qudaamah said: Everyone whose home is within in the Haram is like a Makkan and does not have to do the farewell tawaaf. Al-Mughni, 3/237.
But if a person who lives in Makkah wants to travel after doing the rituals of Hajj or ‘Umrah, then he has to do the farewell tawaaf before leaving Makkah.
Al-Nawawi (may Allaah have mercy on him) said: Our companions said: whoever has finished his rituals and wants to stay in Makkah, does not have to do the farewell tawaaf. There is no scholarly difference of opinion on this point, whether he is one of its inhabitants or a stranger. If he wants to leave Makkah and go back to his country or somewhere else, then he has to do the farewell tawaaf. Al-Majmoo’, 8/254.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: If a man is one of the inhabitants of Makkah, and he does Hajj then travels after Hajj, then he should do the farewell tawaaf, because the Prophet (peace and blessings of Allaah be upon him) said: “None of you should leave until the last thing he does is to circumambulate the House.” Muslim, 1327. This is general in application. So we say to this person who lives in Makkah: So long as you are travelling during the days of Hajj, and you have done Hajj, then do not leave until you have done tawaaf. Al-Fataawa, 23/339.
Based on this, then the lady who asked this question has to do the farewell tawaaf when she wants to travel, after she has done the rituals of Hajj. And Allaah knows best.