Preheat the grill and set the oven rack about 15cm from the heat source. Toast muffin halves under grill until golden, about 2 to 3 minutes. Mix garlic, butter and basil together in a small bowl; spread butter mixture evenly onto each toasted muffin half.
Combine tomatoes, olives and tomato paste in a large bowl; set aside. Whisk together the olive oil, lemon juice and honey in a small bowl. Spoon some of the tomato mixture onto each muffin, drizzle the olive oil mixture over the top, place a piece of mozzarella on top of that and season with salt and pepper.
Return muffins to grill; cook until the cheese has melted, 1 to 2 minutes. Serve immediately.