A: Do you want some tea?
B: No, I don't want . . . . . . . . Thank you!

Statement 'A' asks a question and statement 'B' answers it. The answer given by 'B' is negative and thus the sentence 'B' should stay negative. Thus, the answer must be positive since two negatives make a positive. Also, we can see that the answer is an indefinite pronoun that introduces an object in 'B'. Thus, the answer is a positive indefinite pronoun.
Option A is incorrect. 'nothing' is a negative indefinite pronoun. Thus, it makes the sentence positive. Further, it also makes the sentence grammatically incorrect.
Option B is incorrect. 'none' is not an indefinite pronoun. Further, 'want none' does not make any sense and so 'none' cannot be the answer.
Option C is correct. 'anything' is a positive indefinite pronoun that keeps the statement 'B' negative. It introduces the object to the sentence and justifies the answer 'No' by indicating that the subject does not want anything.
Option D is incorrect. 'something' is a positive indefinite pronoun but it cannot be used here as it does not justify the answer 'No'. It indicates that there is something that the subject might want. Thus, it contradicts the answer given by 'B'.