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Prepare grill for cooking.
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Make the dressing: whisk together 2 tablespoons lemon juice, 3 tablespoons oil, half oregano, half garlic, salt and pepper in a large bowl. Gently stir tomatoes, cucumber and onion into dressing and let stand at room temperature while grilling.
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Marinate the shrimp: whisk together remaining 2 tablespoons lemon juice and remaining oregano, thyme and garlic in a large bowl. Stir in shrimp until well coated and marinate at room temperature for 10 minutes.
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Meanwhile, grill pitas and bell pepper: lightly brush pitas and bell pepper on both sides with oil and season with salt and pepper. Grill pitas on an oiled rack 5 to 6-inches over glowing coals until browned and slightly crisp, about 2 minutes on each side, then transfer to a rack to cool (pitas will continue to crisp as they cool). Grill bell pepper until just softened, about 1½ minutes on each side.
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Grill the shrimp: add remaining tablespoon oil to shrimp and toss to coat. Thread 4 shrimp lengthwise in the same direction (so shrimp will lay flat on grill) on each skewer without crowding. Season with salt and pepper. Grill shrimp until just cooked through, about 2 minutes on each side.
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Break pitas into bite-size pieces and coarsely chop bell pepper. Remove shrimp from skewers and gently stir into tomato mixture with pitas, bell pepper and feta. Add salt and pepper to taste.