Dare I say...
Lady Itoh is Mizu's mother.
I know this has been mentioned before but the resemblance is striking. I have a working theory on how this can be so. Once I've gathered all the pieces I'll expand upon it fully, but a summary is that Lady Itoh had a brief affair with a white man, fraternal twins are born, one can pass fully japanese as the Shogun's younger son, the other cannot. A few people know, the Shogun is not one of them. Someone wants this child dead and has the means to place a hefty bounty on a blue eyed girl, someone wants this child to live and has the means to pay off a maid to hide her. And I know Fowler tells Mizu one of the remaining two white men killed her mother, this is the biggest hole in this theory, however he may or may not be telling the truth or a version of it, and the creators did mention in passing hint that some people we thought dead may not be.