Is the questioner considered sinful for giving her aunt a gift (Quranic tapes) with the intention of ongoing charity, given that the aunt refused to accept it if she had paid for it, and how can the questioner preserve the reward of the gift without telling her aunt that she had paid for it?

If your aunt did not stipulate that you should not have paid money for the tapes you gifted her, then you are not obliged to inform her. However, if she did stipulate that, then inform her of the truth of the matter, and clarify to her that what you paid was little and does not affect you, and that giving and accepting gifts is a prophetic Sunnah; for the Prophet, peace and blessings be upon him, said: "Give gifts to one another, and you will love one another," and he also said: "Muslims are bound by their conditions in what is lawful," and that an aunt is in the position of a mother.