The evaluation of conditional language modeling tasks such as abstractive summarization typically uses test data that is identically distributed as training. In real-world practice, documents to be summarized may contain input noise caused by text extraction artifacts or data pipeline bugs. The robustness of model performance under distribution shift caused by such noise is relatively under-studied. We present a large empirical study quantifying the sometimes severe loss in performance (up to 12 ROUGE-1 points) from different types of input noise for a range of datasets and model sizes. We then propose a light-weight method for detecting and removing such noise in the input during model inference without requiring any extra training or auxiliary models, which effectively mitigates the loss in performance, recovering up to 11 ROUGE-1 points.