Wipe the grates of your grill with a bit of olive oil. Just enough so the pizza won’t stick. Preheat the grill.
Meanwhile, prepare the salad topping. Add the arugula, olives, tomato, cucumber, mint leaves, and oregano to a deep bowl. Spoon in the dressing, and toss until well coated.
Prepare the dough for the grill. Sprinkle some flour on a board or counter. Take one half of the dough, and roll it out into a ¼-inch thick rectangle, sprinkling additional flour on the dough and board, only as needed. Repeat with the remaining piece of dough.
Use a pizza peel or the back of a sheet pan to slide the dough onto the grill. Cook until slightly charred underneath, 3 to 4 minutes. Using metal tongs, turn the dough over, and cook on the other side until slightly charred. Remove from the grill.
Sprinkle an even amount of feta cheese over each crust. Divide the salad, scattering it on top of the crust. Cut into slices, as desired, and serve immediately.