Get an outside cat and problem solved.
Winter Grass is actually a very easy weed to kill, but only if it's done at the right time. Winter Grass Weed Killer is diluted with water in a watering can or spraying bottle as per manufacturer's guidelines, and applied to the entire lawn, not just to the area which appears most affected.
It turns brown and more work
Winter grass can just be cut and left over the ground. They are supposed to be cut and left and we slowly move down to protect the roots of the next rise.