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I know this may be a silly question but what exactly is the author trying to connote when using brackets in [t]his manner?

Most likely that the "t" was a "T" in the original text

and [t]his is pronounced tah-hiss when you are called on in class.


squared brackets are used to mark a point where something was changed from the original. for example, say a witness says the following: "I went to the house." If the book was quoting it in mid sentence, it may say something like this:
Billy couldn't have been at the hotel because "[he] went to the house."

That is obviously a really simple example, and in your case, it probably was a capital before, but just know that square brackets are used to show changes from the original.

"This is the first time we are faced with a case like this."
"Justice Edgar. A. Poe noted that "[t]his [was] the first time [they were] faced with a case like this."