Blend yogurt, cucumbers, 2 tablespoons olive oil, dill, lemon juice, garlic, salt, and pepper in a blender until tzatzikisauce is evenly combined.
Heat remaining 1 tablespoon olive oil in a large skillet over medium heat; cook and stir beef in the hot oil until no longer pink, 5 to 10 minutes.
Layer half of each pita with steak, tomato, onion, feta cheese, lettuce, olives, and tzatziki sauce. Bring edge of each pita over the filling and secure with a toothpick.
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