Stack beef steaks; cut lengthwise in half, then crosswise into 1-inch wide strips. Toss with garlic and oregano.
Heat 2 teaspoons oil in large nonstick skillet over medium-high heat until hot. Add onion; stir-fry 3 to 4 minutes. Remove.
Heat 1 teaspoon oil in same skillet over medium-high heat until hot. Add 1/2 of beef; stir-fry 1 minute or until outside surface of beef is no longer pink. (Do not overcook.) Remove. Repeat with remaining beef.
Return beef and onion to skillet; heat through. Season with salt and pepper. Serve in pita pockets with tomatoes, cucumbers and dressing.
Preheat oven to 204 degrees C. Pat dry chickpeas with paper towel, removing any skins that may come off. Gently toss chickpeas with oil, paprika, black pepper, cayenne pepper, and salt.
Spread chickpeas onto a greased rimmed baking sheet and roast for about 20 minutes, until lightly browned but not hard.
Spread some tzatziki onto one side of the pita, then sprinkle in ¼ of the chickpeas and add veggies. Fold in half and enjoy!