Extractive summarization suffers from irrelevance, redundancy and incoherence. Existing work shows that abstractive rewriting for extractive summaries can improve the conciseness and readability. These rewriting systems consider extracted summaries as the only input, which is relatively focused but can lose important background knowledge. In this paper, we investigate contextualized rewriting, which ingests the entire original document. We formalize contextualized rewriting as a seq2seq problem with group alignments, introducing group tag as a solution to model the alignments, identifying extracted summaries through content-based addressing. Results show that our approach significantly outperforms non-contextualized rewriting systems without requiring reinforcement learning, achieving strong improvements on ROUGE scores upon multiple extractive summarizers.