Modern Text-to-SQL semantic parsers struggle when tested on database schemas unseen during the train time. Further, model adaptation to a new database is challenging owing to zero availability of text queries for the target database until the initial deployment of the parser in the real world. We present ReFill, a framework for transferring text queries from existing databases to a target database. ReFill retrieves diverse existing text queries and masks their source-schema tokens, followed by editing and refilling with target-schema tokens for transferring text queries to the target schema. We show that this process leads to significantly more diverse text than achievable by using an SQL-to-Text generation model trained to directly translate SQL queries into natural text. Experiments across multiple relational databases establish that finetuning a semantic parser on the text synthesized by ReFill offers consistent performance gains over prior data-augmentation methods.