When quoting something, you are representing that this is what the source of the quote said precisely. As a result, if an alteration to the quote is required for any reason, many people use square brackets to indicate that an alteration, however minor, has taken place.
In your example, absolutely yes, square brackets indicate that the 't' was originally capitalised in the source, but has been altered to lower case.
Other examples can include changing the form of a verb:
Yesterday, the Prime Minister said that he "[wants] to lead the country into a new age of prosperity".
Here the original quote might have been "I want to lead the country into a new age of prosperity"; we use square brackets to show that the form of the verb was altered.
This can similarly be used to change things like pronouns into the equivalent names they reference, or otherwise to tweak the grammar to make a short section of a quote make sense in the context in which it will be used.
Ellipses, sometimes but not always also placed in square brackets, can also be used to indicate that the quote has been shortened. This will often also be accompanied by words in square brackets that have been rewritten to make sense in the new shortened quote. So a silly example like:
"I want to lead the country into a new age of prosperity. I saw a survey the other day, while I was reading the morning paper, which said that nine out of ten people believe this country is not as prosperous as it could be."
Might be shortened like this:
"I want to lead the country into a new age of prosperity. [...] [A survey] said that nine out of ten people believe this country is not as prosperous as it could be."
The final use of square brackets in quotes is with the word sic which indicates that a quote is exactly as written, and that something that appears like it might be an error was actually present in the original quote. This is the same regardless of whether the apparent error is actually an error — it can be used both to point out an actual error in the original, and to point out something that looks like an error but isn't. Therefore sic can be used when something looks erroneous regardless of whether you know for sure that it was an actual error.
For instance, you might see something like:
"Despite the constant negative press covfefe [sic]"