Step 1: Understanding the sentence.
The sentence involves a prepositional phrase "between" that requires the objective case "me" rather than the subjective case "I."
Step 2: Analysis of options.
- (A) between Paarin and me about the dent in his car continued: Correct. The phrase "between me" uses the objective case correctly.
- (B) between Paarin and me about the dent in his car continued: Same as (A), correct.
- (C) between Paarin and I about the dent in his car continued: Incorrect. "I" is incorrect after the preposition "between," which should be followed by the objective case.
- (D) about the dent in his car continued for Paarin and I: Incorrect. This changes the sentence structure unnecessarily and incorrectly uses "I" instead of "me."
- (E) about the dent in his car continued: Incorrect. This is incomplete as it leaves out the necessary introductory prepositional phrase.
Step 3: Conclusion.
The correct answer is (A) between Paarin and me about the dent in his car continued.
Final Answer: \[ \boxed{(A) \, \text{between Paarin and me about the dent in his car continued.}} \]