How to decline a sitter gracefully without them feeling offended

Why do you need to go into detail or specifics? If you don’t think they’re suitable just tell them you went with another sitter. That’s totally fine. Most pet parents here don’t even bother to respond personally to applications, either to initially acknowledge the application or to then decline the application. That’s annoying after a sitter has spent a lot of time telling the pet parent everything about themselves.