the reason they have so many cats is that cats have...kittens.
Here in the Philippines, we finally got mama cat fixed after her 4th litter in four years...24 kittens we had to give away.
Hope it works: We paid to fix two female dogs, and they still have puppies every year...but puppies are easier to give away: our dogs are friendly but make good watch dogs for protection (no guns allowed in the Philippines).
Get your money back then...