Preheat an oven to 375 degrees F (190 degrees C). Butter a 2-quart casserole dish.
Heat a large skillet over medium heat; cook the sausage in the hot skillet until completely browned, 5 to 7 minutes. Add the onion, celery, and green pepper; cook and stir until tender, about 5 minutes more. Transfer to the prepared casserole dish.
Bring the grits, water, and salt to a boil in a saucepan; reduce heat to medium-low, cover, and simmer until the grits are tender, about 30 minutes. Add to the sausage mixture in the casserole dish and stir; press into an even layer. Pour the soup over the mixture in an even layer. Sprinkle the Cheddar cheese over the soup.
Bake in the preheated oven until the cheese has melted, about 30 minutes.