Human. Between Korvosa being a predominantly human-inhabited city and Ileosa being Chelaxian, I imagine that there would be few/no non-human Gray Maidens.
I ran a game for 2 grey maiden Cavaliers and they did great but the feats I gave them to give them the grey maiden feel made being human a must for a little space in feats too.
So yeah background wise and crunch wise there's 2 good reasons.
While the original Gray Maidens were all humans (and half-Elves?) the Adventurer's Guide does state that after Illeosa the remaining companies of Maidens do accept non-Humans.