it means it was not part of the original quote; either changed or inserted by the quoting party for clarity or grammatical consistency. compare:

the driver told the ice agent to gargle his balls.

there are no quotes, calls into question how much of it is the reporter's wording. here you would probably assume he said "gargle my balls" but if the quote was "fuck off" it would be more ambiguous: is was the actual quote "fuck off" or did he say something like "get the fuck outta here" and the reporter's summarizing?

the driver told the ice agent to "gargle his balls"

the entire thing is in quotes, so did he literally say "gargle his balls"? whose balls? there's a third person involved? this is also essentially lying since quotation marks suggest everything inside is a direct quote.

the driver told the ice agent to "gargle my balls"

the quote is correct but the sentence reads—and especially sounds—like the reporter is talking about their balls.

so the solution here is to change "my" to "[his]" to make it read correctly while acknowledging that it's not part of the exact quote despite the quotation marks.

sometimes words are changed for clarity, for example:

then he says "[journalists] always find a way to spin"

this suggests that the original quote probably had a pronoun instead, like "they always find a way to spin" or maybe he said something like "motherfuckers always find a way to spin". either way sometimes the flow of the article would make the sentence ambiguous unless who "they" or "motherfuckers" refers to is noted.

or sometimes a word is added for clarity or consistency:

"It was incredible to see Zohran [Mamdani] got elected."

this could mean the speaker originally just said Zohran, and the reporter is adding the last name for clarification or consistency with how he's been referred to throughout the article.

sometimes the words are changed to fix the original quote:

"I was shocked when they elected [Mamdani]"

this might be because the original quote was mispronounced or misspelled (“Mandami" or whatever)

or sometimes [sic] is added to point that the error was left in by the reporter deliberately to note that the original quote had the misspelling or mispronunciation:

"I was shocked when they elected Mandami [sic]“

this means the reporter left in the mistake on purpose because the original quote had it, and clarifies that it's not a typo by the reporter. otherwise the reader would be unclear as to whether the original quote was correct but the reporting has a typo, or whether the original quote had it wrong.

finally there's [...] which means parts of the original quote were cut out for brevity or again clarity. maybe the original quote was too rambling or confusing.

Unlike linguists, Grass “…always wonder[s] what the square brackets [are] about in newspapers but never enough to look it up”

:)

It's when you quote someone but change the words slightly to fit the sentence structure/context you're adding it in

That's not what it's for at all, so ignore them. It was probably "gargle my balls". The brackets indicate an intentional changing of phrase to make a quote work in a different context.

Driver told agent to "gargle [his] balls"

Another example might be replacing pronouns with proper nouns. Like if someone says "I told them what brackets are for in quotes" it might get changed to "I told [Grass] wheat brackets are for in quotes."

Lastly, I'll explain [sic]. It's some Latin phrase (doesn't matter what for) but it's used to denote an intentionally odd thing in a direct quote that isn't a typo. Like if someone says "irregardless I was it to happen" then it might get quoted as "irregardless [sic] I want it to happen" to indicate that the author didn't make a mistake, but the speaker did.