Meet and greet with client's dog and my cat?

What did the person say about their dog? And has your cat been exposed to dog she doesn't know? One month is a long stay. It's absolutely necessary to introduce the dog to your cat in your house to see how it goes. But don't forget most dogs act differently when the owner is present. And their behaviour can change when the dog is alone with you and your cat.
I would make sure their dog has been around cats before and is absolutely OK with them. Good luck.

I don't have a cat - or any other animals currently - but I agree it is critical that this dog meet your cat. I understand why you don't do Meet & Greet's in your home. But I always have them in my home because I want the dog(s) to get to know the smell of my home and the owners to get a feel for the environment. I almost always have other dogs here when I do Meet & Greets. I would recommend a few things to improve the likelihood that it's a good fit. Definitely do as Lenka suggested and ask the owner what the dog's experience is with cats. If the dog has not had much experience and the owner just thinks they'll be fine, you may or may not want to go through with the Meet & Greet. However, I've found that most owners would not willingly put their dogs somewhere where the dog might become aggressive. They want their pet to be as comfortable as possible. If you do the Meet & Greet I would find a way to have the cat "unreachable" to the dog, yet still accessible by sniff. For example you can have your cat in a crate if he/she doesn't freak out (I know cats don't always like them). If it's possible you can either be holding your cat or have someone you trust holding your cat. If you have a baby gate that separates areas you can have that closed with your cat on the other side (that's what I have in my home). I would also say if you're really nervous about the meeting, both the dog and cat will pick up on it. If you feel you'll be worried the whole time the dog is there it might be best for you, your cat, and the dog if you decline to take the dog. There is nothing wrong with not accepting a dog and owners generally appreciate if you tell them you think the dog would be happier elsewhere. I hope that helps! Good luck!