The goal of text-queried target sound extraction (TSE) is to extract from a mixture a sound source specified with a natural-language caption. While it is preferable to have access to large-scale text-audio pairs to address a variety of text prompts, the limited number of available high-quality text-audio pairs hinders the data scaling. To this end, this work explores how to leverage audio-only data without any captions for the text-queried TSE task to potentially scale up the data amount. A straightforward way to do so is to use a joint audio-text embedding model, such as the contrastive language-audio pre-training (CLAP) model, as a query encoder and train a TSE model using audio embeddings obtained from the ground-truth audio. The TSE model can then accept text queries at inference time by switching to the text encoder. While this approach should work if the audio and text embedding spaces in CLAP were well aligned, in practice, the embeddings have domain-specific information that causes the TSE model to overfit to audio queries. We investigate several methods to avoid overfitting and show that simple embedding-manipulation methods such as dropout can effectively alleviate this issue. Extensive experiments demonstrate that using audio-only data with embedding dropout is as effective as using text captions during training, and audio-only data can be effectively leveraged to improve text-queried TSE models.