Hmmmm...let's see; Does he own it? No. Does Egypt own it? No. Then he has no claim on it and should make no pretensions of such.
The Metropolitan Museum built an addition in the early 1980’s to house artifacts on indefinite loan from the Government of Egypt. This was around the time that the King Tut artifacts were touring the U.S. to packed houses and long lines. He could legimately threatened to recall those.
The Brooklyn Museum long had the country’s best Egyptology collection, built up one item at a time over a century, but they were instantly eclipsed by that loan. In a sense this would restore the Brooklyn Museum prestige, but it would be a loss for New Yorkers and the rest of America.