Is that maid is actually sent by someone else to use her as a hostage against Dietrich, because she's too much of an idiot to realize such possibility.
So Dietrich went and threaten whoever is behind the maid to stop this shit if they want to live another day.
Also, to paraphrase Myne from bookworm on why she doesn't care to get rid of the 'spy' in her case (Lancel in this case):
I'd rather deal with someone so simple like this than having to be wary against someone smart enough to hide their hostility.