The word "refute" means to prove a statement or theory to be false or incorrect. In this context, the sentence indicates that despite the speaker's attempts to disprove or challenge the charges against them, the sister tried to do something opposite. The word that is most nearly opposite in meaning to "refute" and appropriately fills the gap is "maintain." In this context, "maintain" suggests supporting or upholding the charges, thus contrasting with the speaker's attempts to refute them. Therefore, option D, "maintain," is the most suitable choice.