The gameplay loop is pretty solid, but i feel it could use a few tweaks. First off, the game's very boring in my opinion (these types of games aren't really for me, so i don't know about the majority of other people.) Most of the time, you're clicking on each pet and seeing if you can pet/groom them. I feel like there's way too much time between getting a message or a new pet at the door, so I'd lower that a bit. You also aren't able to back out of your phone after you send a pet, which gets annoying pretty quick lol.
Again, this genre of games never really interests me, but the gameplay was simple enough for me to immediately understand and it fits with the theme very well, so great job on that!