Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we would like to thank you for the great confidence you place in us, and we implore Allah Almighty to help us serve His cause and render our work for His Sake.
While performing the Hajj rituals, a pilgrim should follow the exact example of the Prophet (peace and blessings be upon him) who said: "Learn your rituals from me." (Reported by Ahmad and An-Nasa'i) It is known that the Tawaf rounds are to be started at the Black Stone.
The Hijr Isma`il is a low semi-circular wall that encloses a small area on one side of the Ka`bah. The correct path of Tawaf should be around the Ka`bah and the Hijr. The pilgrim should not enter the area enclosed by the wall while doing Tawaf.
Responding to your question, Sheikh Ibn `Uthaymeen, a prominent Saudi Muslim scholar, (may Allah shower mercy on his soul) issued the following fatwa:
This is a very serious mistake, when some people enter through the gate of the Hijr when doing Tawaf and exit through the other gate when it is crowded, thinking that this is easier. It is a serious mistake because the one who does that is not considered to be doing Tawaf around the Ka`bah. Allah says: (and circumambulate the Ancient House (the Ka`bah at Makkah)) (Al-Hajj 22: 29).
The Prophet (peace and blessings be upon him) circumambulated the House from outside the Hijr. If a person circumambulates the Ka`bah going inside the Hijr, he is not regarded as having circumambulated the House, so his Tawaf is invalid. This is a serious matter, especially since Tawaf is a pillar (essential part) of both Hajj and `Umrah. The answer to that is that we should explain to the pilgrims that Tawaf is not valid unless it encompasses the entire Ka`bah, including the Hijr.
There are some people who do not make sure that they keep the Ka`bah on their left. You see them doing Tawaf with their women folk, and they hold hands with their brothers or friends to protect the women, so you see them doing Tawaf with their back towards the Ka`bah, and his brother or friend doing Tawaf facing towards the Ka`bah. This is also a serious mistake, because the scholars say that one of the conditions of Tawaf being valid is that the Ka`bah should be to one's left, and if you have your back toward it, or face it, or walk with it to your right, then this Tawaf is not valid.
What people should do is to pay attention to this matter, and strive to make sure the Ka`bah is to their left throughout Tawaf.
There are some people who put their backs to the Ka`bah or face it for a few steps because of the crowding. This is also a mistake. People should be on the safe side with regard to religious matters and acknowledge the boundaries set by Allah with regard to worship and avoid mistakes so that they will worship Allah with knowledge.
Does it not astonish you that if a man wants to travel to a land that he does not know, he does not travel until he has asked about it and tried to find out the easiest way to get there so that he can reach it comfortably and with ease without getting lost, but when it comes to matters of religion, many people, unfortunately, start their worship and do not know the limits set by Allah. This is a shortcoming and, indeed, is negligence.
Excerpted, with slight modifications, from: www.islam-qa.com
Allah Almighty knows best.