Could the cat be pregnant in January or is the house owner mistaken ?
With cats, ANYTHING is possible. The thing to look for are the nipples. If they are large and pink, then it is possible.

If she isn't too far along, the kittens can be aborted. I know this sounds kind of awful, but it's done all the time. They remove everything, the plumbing (ovaries, tubes, etc.) the whole uterus intact with the fetuses in it. The kittens never take a breath, never meow and are not alive.

There is nothing different about trapping a pregnant female. Is she feral? Is your neighbor able to pick her up and pet her? Are her older kittens feral? Do they respond to her? If they are terrified of her when she approaches, then they are feral. Unless this woman wants to spend the time (it takes a LONG time to tame feral cats that have been out in the wild) to socialize them, then she's wasting her time keeping them.

Socializing them takes time, patience and alot of love. Unfortunately, feral cats are deemed unadoptable by shelters.

When you do trap her and her kittens, you need to not feed themfor 24-48 hours. This will make them very hungry. Place the trap in the area where they are known to hang around. Put staw inside the trap to disguise the trip plate and the metal mesh. Set the trap and put a towl over it so they don't see it. Cut a piece of paper plate in the shape of a piece of pie. Put the smelliest sardines or canned cat food you can find in the back of the trap, past the trip plate. Make sure you check the trap. Better yet, go somewhere where you can't be seen, but can view the trap. It's a waiting game.

I'm sure other people here can give you more advice than I can. I wish you alot of luck. It takes a big person to step up and do what you're doing. I commend you, PIF!! Please keep us posted!