Answer: B. It is important to remember that “[w]hen [he] refer[s] to integrity, [Carter has] something very specific in mind.”
The option that uses brackets correctly is option B. Brackets should be used whenever you are altering words in a direct quotation without significantly changing the meaning of the quote. In this case, option B is the only one that changes words that are within quotation marks (because they are a direct quote) while maintaining the meaning of the quote.