Shred cucumber. Combine yogurt, mint, lime juice, 1/8 teaspoon salt, garlic, and cucumber in a small bowl, set aside.
Place chickpeas in a single layer on paper towels. Cover with additional paper towels; pat dry. Heat a large skillet over medium-high heat. Add 2 tsp oil to pan; swirl to coat. Add chickpeas to pan; sauté 10 minutes or until lightly browned and crispy, stirring frequently. Remove chickpeas from pan using a slotted spoon; drain on paper towels.
Combine remaining 1/2 teaspoon salt, chickpeas, cumin, paprika, and red pepper in a medium bowl; toss well to coat.
Combine 1 tbsp olive oil, lemon juice, and black pepper in a small bowl, stirring well with a whisk. Add arugula; toss gently to coat. Add chickpea mixture; toss to coat.
Fill each pita half with about 2/3 cup chickpea mixture, a couple tomato slices, and 2 tablespoons sauce. Serve immediately.