Turn all burners of a gas grill on high or build a charcoal fire. Meanwhile, lay sliced tomatoes on a baking sheet. Mix 1 tablespoon of the oil with the minced garlic. Drizzle oil over tomatoes; set aside.
Without punching or kneading dough (which makes stretching more difficult), turn dough onto a lightly floured surface. Using a dough scraper or sharp knife, quarter dough crosswise. Working one at a time, stretch each portion into a rustic 12- by 3½- to 4-inch rectangle; transfer to a large cornmeal-coated baking sheet.
Reduce grill heat to medium; lift stretched pieces of dough on grill. Cover and cook until bottoms are spotty brown, moving them around and punching dough down as necessary to ensure even cooking, 3 to 4 minutes. Return pizza crusts, grilled side up, to baking sheet, topping each with a portion of tomatoes (reserving any remaining garlicky tomato liquid). Lightly sprinkle tomatoes with salt and top with a portion of mozzarella cheese. Return pizzas to grill; cover and continue to grill until pizza bottoms are spotty brown, 3 to 4 minutes longer. Transfer to a cutting board.
Meanwhile, toss arugula with olives, feta, remaining tablespoon of oil and a light sprinkling of salt and pepper. Drizzle in reserved tomato juice; toss to coat again. Top each pizza with a portion of salad. Transfer to a cutting board, cut into pieces and serve.