I'm sorry if I didn't quite get the joke, but this is not in contex of petting the cat.
I'm guessing they are on their way back from work, so saying "Hi good work today" makes sense.
Similar to how you say excuse me all the time in english, it can be used in a few different situations.
I would say it's the norm to say this with work-related ppl.
E.g. I sometimes talk to an ex-college, from the admins of the place I worked at, and unless it's the early morning, I start off by saying "Otsukaresama desu".
So yeah not that petting the cat is a tough job but them being coworkers makes them say that (^∇^)ノ♪
I meant it as a joke by taking the meaning literally; I found that idea funny. Many things we say on the offhand, rightly assuming that people will understand what we actually meant, can be made quite hilarious by mixing in the literal context.
Like the common joke: What's up? "The ceiling."
But I do appreciate the linguistics lesson! (●'◡'●)ノ
lmao japanese greetings are so silly. like bro really said thank you for your hard work while she was petting a cat