Generative AI tools, particularly those utilizing large language models (LLMs), are increasingly used in everyday contexts. While these tools enhance productivity and accessibility, little is known about how Deaf and Hard of Hearing (DHH) individuals engage with them or the challenges they face when using them. This paper presents a mixed-method study exploring how the DHH community uses Text AI tools like ChatGPT to reduce communication barriers and enhance information access. We surveyed 80 DHH participants and conducted interviews with 11 participants. Our findings reveal important benefits, such as eased communication and bridging Deaf and hearing cultures, alongside challenges like lack of American Sign Language (ASL) support and Deaf cultural understanding. We highlight unique usage patterns, propose inclusive design recommendations, and outline future research directions to improve Text AI accessibility for the DHH community.