I’ve always used a little squirt of fairy liquid in the mop bucket and then done a second go with clean water.
But there must be a nice smelling pet safe product that doesn’t need rinsing off?
I’ve just got a cleaner for the first time ever and I think she made her best guess from the cleaning cupboard which was dettol liquid. The floor is very clean but not sure it’s good for cats and it smells like a dentist in here 🙈