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In my earlier comments I mentioned

Typically the pronoun they, in this instance, would be italicised, to show emphasis in speech. Sometimes scare quotes are used instead. In the actual episode, did the speaker use air quotes by any chance?

When the OP confirmed that speech/quotation marks were missing, and the actor did not do air quotes, I replied:

No, I wouldn't expect subtitles to go into the trouble of using scare quotes or italics. I suspect Speaker B stressed they and gave a quizzical look

The Oxford Dictionary provides the following definition

scare quotes
Quotation marks placed round a word or phrase to draw attention to an unusual or arguably inaccurate use.

So, if we look at the first line cited by the OP we see that the name of an organisation is used, Hessington Oil (I've capitalised Oil because it is part of a proper noun). In American English — and Suits is an American TV series — organisations and companies are often used in the singular. For example,

  • Microsoft is one of the industry leaders in accessibility innovation...
  • The Coca-Cola Company has on occasion introduced other cola drinks under the Coke name.

It could be that speaker B believes that "they" refers to a company or an organisation, and as a result uses the singular verb in: “Who is they?”