Well that was a blast from the past...
Following a fakeout where it's theorized that the mysterious woman popping up in episode after episode may be the long lost Susan Foreman (last seen in the episode "The Five Doctors" in 1983), it turns out they were the villain Sutekh, last seen in the episode "Pyramids of Mars" in 1975.
https://en.m.wikipedia.org/wiki/Susan_Foreman
https://en.m.wikipedia.org/wiki/The_Five_Doctors
https://en.m.wikipedia.org/wiki/Pyramids_of_Mars
Season Finale next week!
I'm thinking Susan too or maybe The Doctors daughter.
We saw with River Song that she went from Melody Pond to River Song due to a miss translation, so Mrs. Flood has to be connected to River somehow.