Text-to-SQL parsers typically struggle with databases unseen during the train time. Adapting Text-to-SQL parsers to new database schemas is a challenging problem owing to a vast diversity of schemas and zero availability of natural language queries in new schemas. We present ReFill, a framework for synthesizing high-quality and textually diverse parallel datasets for adapting Text-to-SQL parsers. Unlike prior methods that utilize SQL-to-Text generation, ReFill learns to retrieve-and-edit text queries in existing schemas and transfer them to the new schema. ReFill utilizes a simple method for retrieving diverse existing text, masking their schema-specific tokens, and refilling with tokens relevant to the new schema. We show that this process leads to significantly more diverse text queries than achievable by standard SQL-to-Text generation models. Through experiments on several databases, we show that adapting a parser by finetuning it on datasets synthesized by ReFill consistently outperforms prior data-augmentation methods.