The correct option is D let them down
A phrasal verb is a verb combined with an adverb or preposition to
provide a meaning different from the literal meaning of that individual
verb. The underlined phrasal verb 'let in' means 'to let someone in the house' or 'to share your feelings with someone'. It isn't relevant to the given statement hence option A is incorrect. 'Let down' in 'let them down' means 'to disappoint someone', here it refers to disappointing 'them', the clients, it's relevant to the statement hence option C is correct. 'Let out' means 'finish, to let someone leave' as in 'her lectures let out soon today'. It isn't relevant to the given statement, hence option B is incorrect. 'Let go' means 'to set someone/something free'. As it doesn't provide the required meaning to the sentence, option D is incorrect.