Document digitization is essential for the digital transformation of our societies, yet a crucial step in the process, Optical Character Recognition (OCR), is still not perfect. Even commercial OCR systems can produce questionable output depending on the fidelity of the scanned documents. In this paper, we demonstrate an effective framework for mitigating OCR errors for any downstream NLP task, using Named Entity Recognition (NER) as an example. We first address the data scarcity problem for model training by constructing a document synthesis pipeline, generating realistic but degraded data with NER labels. We measure the NER accuracy drop at various degradation levels and show that a text restoration model, trained on the degraded data, significantly closes the NER accuracy gaps caused by OCR errors, including on an out-of-domain dataset. For the benefit of the community, we have made the document synthesis pipeline available as an open-source project.