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RiseOne: This is the only explanation i could come up with.
Training or Maintaining of Assassins by Noble's isn't that odd and almost everyone did it (even religious or government organizations do it), both for good and bad work. And turning an Orphan into a Assassin is probably the best method, since Orphan normally don't have any connections, plus it gives them a job to do (especially if the Orphan is a girl), because there aren't that many job options if you consider the era setting of the plot. Also, probably that Elf girl is more suited for these kind of dexterity related work (like MC is trying to get her to be a blacksmith, while that Old Lady only knew about using her as an Assassin to let take advantage of her base skills).
What matters here is
why did she put a Brainwashing term of, "not trusting the new master", on that Elf girl.
That just feels odd, because what's the use of putting brainwashing term like that on a Assassins, even though the user already knew that they were going to die because of the secret that even her Assassin knew about.
Its probably so that, because of the Brainwashing, Elf girl won't be able to divulge any of the information she knew about (even after heavy torture), including the secrets both good and bad which could have worked in favor of the people who got that Old Lady killed. It could only be seen as an act of saving and protect that Elf girl's life, because if that Old Lady was actually ruthless and evil, she could have probably commanded the Elf girl to kill herself using her Brainwashing, which she didn't. And its possible that the Noble who got that Old Lady killed is still keeping the Elf alive because he believes that she knows something which could be useful for him, but can't get it out because of the Brainwashing (so just waiting for a chance until the Brainwashing gets removed).