Edith herself made arrangements with tenant farmer Timothy Drewe to take Marigold at the very end of the 2013 Christmas Special. Mr. Drewe was indebted to the Crawleys both for allowing him to take over his father's tenancy and for giving him the an additional job in overseeing the pig farming operation. Edith thus thought his family could be trusted to raise her daughter (although she did not initially admit to being the mother).
As for Bates and Mr. Green, while Bates had his suspicions all along, Green saying that he went downstairs during the concert because he could not stand the screeching sealed it. Green was pushed in front of a bus while in Piccadilly Circus.