Summary: Madame Vastra keeps her true appearance hidden.
Madame Vastra is London’s greatest detective; her exploits are legendary thanks to the writings of Doyle, although of course Doyle writes his detective as a man. Equality between men and women is a long way off, but Vastra believes it will eventually become a reality.
Meanwhile, she hides her face behind a heavy veil when she leaves her home to go about her business; if people would be disturbed about a woman carrying out investigations into crimes, how much more dismayed would they be to know she is of a different species entirely?
Under the circumstances, her disguise seems prudent.