The Riddle of the Sphinx

Firmly on the tourist trail this morning, at Cleopatra's Needle.
The story of the artifact's dramatic journey from Alexandria to London is well known (but click here if you're unfamiliar with the story & would like to read about it).
What I learned only recently concerns the pair of Sphinxes at the Needle's base.
Legend has it (& I'm not one to doubt legend) that they were supposed to be facing outwards, guarding the Needle, but were mistakenly installed the wrong way round.
So they appear to be keenly eyeing the pillar like it is a huge scratching post!