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Existing distantly supervised relation extractors usually rely on noisy data for both model training and evaluation, which may lead to garbage-in-garbage-out systems. To alleviate the problem, we study whether a small clean dataset could help improve the quality of distantly supervised models. We show that besides getting a more convincing evaluation of models, a small clean dataset also helps us to build more robust denoising models. Specifically, we propose a new criterion for clean instance selection based on influence functions. It collects sample-level evidence for recognizing good instances (which is more informative than loss-level evidence). We also propose a teacher-student mechanism for controlling purity of intermediate results when bootstrapping the clean set. The whole approach is model-agnostic and demonstrates strong performances on both denoising real (NYT) and synthetic noisy datasets.