Granted, I'm only a casual speaker/writer of English, but I don't see why you'd want an apostrophe. "The acquaintance of it" ought to be swapped out for "its acquaintance", even when "it" refers to a specific individual. Is there some super secret grammar rule I don't know about?

Its only a matter of time before I make this infamous error again.

Your reader is correct; you don't use apostrophes with possessive pronouns.

2015 NO REGERTS!

You can't gloat over this, you know, since it is SO ambiguous. There has got to be a way to make it less so. "It" is almost a name, so maybe capitalize it? Or an asterisk, or quotations around it? Or restructure the sentence? Because by far the most obvious interpretation is the regular old "its acquaintance."

1) regrets making "It's" acquaintance.
2) regrets making "It"'s acquaintance or it's acquaintance or it's* acquaintance (*where I met someone who called themselves "It")
3) regret making the acquaintance of "It."
4) or other solutions, because I'm a stickler for non-ambiguous writing. Like any good editor should be.

Thank you @1. And Four needs to look at the article.

@6: I had read the article when it came out, and remembered that "it" was used as a pronoun for the individual in question and not as a name. However, your comment made me re-read the article to see if I had misinterpreted it. But the article states that "this person's preferred pronoun was 'it.'" So I disagree that it is a name at all in this context, let alone almost a name, and consequently stand by my smug grammaring.

Sure it's not a name...I was trying to come up with a solution to the ambiguity. "'It's' acquaintance" is the correct spelling based on what they were trying to convey, though. Meaning, the "acquaintance of it," yes? That would be "It's" acquaintance. But, see, it's a trap. A trap that caught you and me and several others. An ambiguity black hole that could have been solved with a slight restructuring of the phrase.