Heat a grill pan over medium-high heat. Coat pan with cooking spray. Sprinkle both sides of steaks evenly with salt and pepper. Add steaks to pan; cook 4 minutes on each side or until desired degree of doneness. Let steaks stand 5 minutes. Cut steaks diagonally across grain into thin slices.
Combine mayonnaise, mustard, Worcestershire, and garlic in a small bowl, stirring well with a whisk. Spread about 1 tablespoon mayonnaise mixture on each of 4 slices of bread; divide steak evenly among bread slices. Top each serving with 1/4 cup arugula and 1 bread slice.