Preheat a grill to medium high. Toss the shrimp and onion (optional) in a bowl with the olive oil and oregano. Season with salt and pepper.
Stretch the pizza dough into a roughly 8-by-10-inch rectangle. Lightly brush the grill with olive oil. Lay the dough on the grill and cook until the top begins to bubble and the bottom is marked, about 3 minutes. Remove with tongs and put cooked side up on a cutting board. Brush with olive oil.
Grill the shrimp and onions, turning, until onions softens and shrimp are lightly charred, about 5 minutes. Top the crust with the shrimp and onions, then slide the pizza back on the grill. Top with the tomatoes and feta, cover and grill until the dough is cooked through and the cheese is soft, about 5 minutes.
Carefully transfer the pizza to the cutting board. Sprinkle with the parsley and cut into pieces.