Do potential clients see your booking scores when they search for sitters?

I'm running into the same issue. I'm archiving clients who aren't a good fit, which always ends up being because they don't actually read my profile regarding what I won't allow (unaltered dogs and aggression to cats) or because they don't respond to my questions. My score shouldn't drop because they're not responding or aren't appropriate.

No, they do not.

Having to archive due to owner or dog(s) not a good fit happens to all of us. I ignore scores because they change so frequently. Set your goal for repeats that are a Great fit. Advertise to bring in potential new customers. Places to advertise would be Nextdoor.com, Pet friendly Apts, Hotels, search for local Business 2 Business (aka B2B) groups and join, connect with rescues, dog trainers and realtors that are hosting an open house in your area. Make sure to be professional and leave your business cards. It may take time but you will start to get "potential" new customers. Still, be prepared to archive some owners. As for the owner that wanted to do a meet & greet for sometime in the future, do it! Give them your business card. They may just come back if you believe their pup(s) would be a good fit.