Final answer:
The correct phrase is 'which manage', as 'which' refers to companies, while 'who' is used for persons. This distinction is important for clarity and grammatical accuracy in written English.
Step-by-step explanation:
The correct phrase to use in the context provided is 'which manage'. Companies, as non-human entities, are referred to by the relative pronoun 'which', not 'who'. 'Who' is used for persons. Therefore, the sentence should read: 'The two companies, which manage most private detention centers, insist they aren't trying to influence immigration policies.' This grammar rule helps provide clarity and accuracy in written communication.
The discussion of the actions taken by the different administrations illustrates the complexity of immigration policies and the different approaches they've taken to manage detention centers and the immigration processes. These directives have had a significant impact on how these private companies operate and the overall narrative around immigration in the United States.