What to do with a cat that has to nurse but doesn't have any kittens?

First of all, excuse my poor English.
So I have a cat who recently had kittens, but the owner of our house gave them away too early without my permission, she still has a lot of milk and her breasts are all sore and swollen. I'm thinking that she really needs to get that milk out. My neighbour owns a cat that recently had kittens too and seems to be rejecting one of them, because she brought the kitten to our door and when we took him back to her she just ignored him and started playing with me instead. Do I make my cat nurse my neighbour's kitten? I'm really worried that if I don't do anything my cat might have a health issue. Really need advice here.

Nursing your neighbor's kitten is an excellent idea! You should bring him to your cat immediately!

How old were the kittens your landlord took away? Why do you think he took them? Did he just enter your home and take them? This is concerning. Where do you live?

Aw, adopting the kitten is a great idea. Can you make sure that this kitten is weaned at an appropriate age?

Can you also ensure that your cat stays inside and away from intact males until she can be spayed? She can already get pregnant again, and without going into heat. I'm sure this is very upsetting!

My landlord is one of those people who think the best you can do for an animal is feeding them from time to time and that's it. He doesn't really feels love for them he just feeds them. I talked to him about it and he said that he gave them away because some people wanted the kittens and that's fine but he should have asked me first. He also has a dog who has a bloody nose and he never did anything about him so i had to take him to the vet today. I'm spending a lot of time and money taking care of my and his pets.
So about the kitten, it seems that my neighbours cat is nursing her kitten now, the cat still comes to my house from time to time but she is giving her kitten at least some kind of attention. So I'm not sure what to do now. Is it okay if I just milk the cat? I know it sounds funny but it really worries me, her breasts are so bad looking, I might upload a picture when I can.

A cat's milk usually dries up in about 2 weeks after stopping nursing.

However, why don't you take your own cat to the vet? They may be able to give the cat something to help her milk dry up. Perhaps she has mastitis, which is infection, and needs antibiotics to clear up.

In the meantime, do NOT milk your cat. That will not help matters. You can put a warm, damp compress on her nipples to give her some relief.

Call your vet, and go ahead and schedule her spay as well.

I'm still puzzled as to how your landlord had access to your kittens.