Pre-trained retrieval models often face challenges in zero-shot retrieval for knowledge-based question answering, as different tasks rely on different corpora. We introduce SQUARE (Synthetic QUery-based Adaptive REtrieval), a novel method for corpus-specific unsupervised retrieval customization. SQUARE leverages LLMs to generate grounded synthetic question-answer pairs from the corpus, which are then used to fine-tune the retriever. A filtering mechanism based on the synthetic answers is employed to ensure high quality of tuning data. Extensive experiments on various datasets demonstrate superior performance of SQUARE compared to zero-shot retrieval and other customization methods, highlighting the value of corpus adaptation for effective retrieval.