I don't know whether it was the reason why Egypt did not demand Gaza but, unlike Gaza, Sinai was part of Egypt since the Muhammad Ali dynasty (the Albanian Ottoman general, not the boxer). Muhammad Ali and his successors, as nominal Ottoman Viceroys (or Khedives, to use their actual title), claimed to control Egypt (with Sinai) and Sudan, nominally under sovereignty of the Ottoman Sultans.

Gaza however, was part of Palestinian sanjaks instead of Egypt vice-royalty. It was also culturally much closer (along with other Palestinian lands) to Syrian Arab culture, instead of to Egyptian Arab culture. After WW I and partition of Ottoman Empire, Gaza was part of British mandate of Palestine, and not given to Egypt, so the ties with Egypt was not at all that strong.

Egypt did not consider Gaza to be part of its territory. During the years of Egyptian control, Gaza was regarded as a separate territory with its own self rule government. In addition to that, Israel was not willing to withdraw from the Gaza strip