Benchmark Data Contamination (BDC)-the inclusion of benchmark testing samples in the training set-has raised increasing concerns in Large Language Model (LLM) evaluation, leading to falsely inflated performance estimates and undermining evaluation reliability. To address this, researchers have proposed various mitigation strategies to update existing benchmarks, including modifying original questions or generating new ones based on them. However, a rigorous examination of the effectiveness of these mitigation strategies remains lacking. In this paper, we design a systematic and controlled pipeline along with two novel metrics-fidelity and contamination resistance-to provide a fine-grained and comprehensive assessment of existing BDC mitigation strategies. Previous assessment methods, such as accuracy drop and accuracy matching, focus solely on aggregate accuracy, often leading to incomplete or misleading conclusions. Our metrics address this limitation by emphasizing question-level evaluation result matching. Extensive experiments with 10 LLMs, 5 benchmarks, 20 BDC mitigation strategies, and 2 contamination scenarios reveal that no existing strategy significantly improves resistance over the vanilla case (i.e., no benchmark update) across all benchmarks, and none effectively balances fidelity and contamination resistance. These findings underscore the urgent need for designing more effective BDC mitigation strategies. Our code repository is available at https://github.com/ASTRAL-Group/BDC_mitigation_assessment.