Bring a saucepan of water and salt to a boil, add shrimp, and cook until pink, 3 to 5 minutes. Drain and cool, about 30 minutes. Spread out cooled shrimp on a serving platter and top with 1/2 the mayonnaise.
Mix grated eggs and remaining mayonnaise in a bowl and spread on top of the shrimp. Sprinkle with pineapple pieces. Top with Cheddar cheese.