I am currently on a pet-free sit and very early on I was visited by a cat (he hopped through an open window). He was friendly and curious, and I gently directed him to the exit door. The visits are now almost daily, and I never ever feed him anything, but will pet him and guide him out. I contacted the person on his collar, and he very politely joked about the current petsitter being mock jealous and that was that. I am tempted to leave a note with the sitter just to introduce myself in a manner of friendly neighborly-ness, but mostly because if I were on a sit and the cat was gone a lot, I would start to worry a little. He has never slept in the house, but he will sit with me on a back stoop while I read. This could very well be a case of overthinking, so please be gentle with me. Thanks!
Just reach out and tell them the situation.
It’s not like you are perma banned from speaking to other people, just because you are on a house sit.
I don’t think the sitter is worried if it’s an indoor/outdoor cat. Cats can be gone for hours and only come back to eat or sleep in a safe warm place. I say knock on their door and introduce yourself. You are both sitters and have that in common. It would be funny if the sitter was also from THS. Invite them over for a glass of wine, a beer or for tea. Probably the house you are staying in welcomed that cat in so the cat keeps coming back. Who knows if they gave the cats treats. No screens on the window which in some countries are common.
the world could use more of this… friendliness for the sake of it. 
Enjoy your housesit that comes with a kitty that you don’t have to take care of!
I sat a cat and dog - and the cat had a flap (the dog was too big to fit through the flap). The cat and the next door cat would visit back and forth often for dinner parties. Some days I’d not see the cat I was sitting, sometimes I’d have the neighbor cat visiting for meals.
That sounds like a cute children’s book you can write.
UPDATE: I left a very brief intro note saying hello and it’s been crickets… But oh well! I do not regret being friendly.
That was nice of you. You’re right, nothing to regret.