Heat grill to medium-high. Lightly brush fish with olive oil, and season to taste with kosher salt and black pepper. Grill fish over direct heat until firm and opaque throughout, about 4 to 6 minutes per side. Fish should flake easily but remain moist. Brush bread lightly with olive oil, and grill until slightly toasted. Rub the cut side of garlic cloves over the bread.
Combine mayonnaise and mustard. Spread mayonnaise mixture on 4 slices of bread. Top with arugula, fish fillets, Grilled Puttanesca Salsa, and remaining bread slices. Serve immediately.