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Heat grill to 350°F.
Place 1/2 the defrosted dough on an oiled baking sheet. Stretch out the dough to form a rough rectangle almost the size of the baking sheet, about 9 by 13 inches. Lift the dough from the baking sheet, from 1 end and carefully place it on the grill. When the bottom is browned, around 3 to 5 minutes, using a tongs, turn the pizza crust over. Continue cooking for about 1 minute, or until the second side begins to brown. Using tongs move the crust to a cooler area of the gill and brush it with olive oil. Add half of the toppings, beginning with the mozzarella, then the tomato, red onion, garlic, olives, and capers. After 2 to 4 minutes, the cheese will be melted. Slide the pizza onto a baking sheet; place half of the arugula on top and season with salt and pepper. Repeat with the other 1/2 of dough.