"According to Makrizi, Rashidi and other medieval Arab scholars, the face of the Sphinx was vandalized in 1378 A.D. by Mohammed Sa'im al-Dahr, a "fanatical sufi of the oldest and most highly respected sufi convent of Cairo." The nose and ears are mentioned specifically as having been damaged at this time. According to one account, Haarmann states, the residents in the neighborhood of the Sphinx were so upset by the destruction that they lynched him and buried him near the great monument he ruined."
-An article by Ulrich Haarmann, "Regional Sentiment in Medieval Islamic Egypt," published in the University of London's Bulletin Of The School Of Oriental And African Studies (BSOAS), vol.43 (1980) p.55-66
I would have difficulty believing that an officer of a Western army would willingly desecrate a great work of art for the fun of it.