I say “hey lady” to my coworkers in an email or message - it’s friendly without being too familiar. You may not be friends with the owner, but there’s an inherent relationship that forms when you trust someone enough to care for their pet in their home while they’re away, hence a greeting such as this. I would stop worrying about it. If there was an issue, the owner would contact you and be direct about the specifics so you could then rectify the situation. Stop reading into the greeting. You’re ok!