Make the dressing: In a small bowl, combine olive oil, ginger, hot sauce, vinegar, garlic, salt, and black pepper. Set aside.
If using bamboo skewers, soak them in cold water for 10-15 minutes. Thread beef and red pepper pieces onto skewers. Brush with remaining olive oil and sprinkle with salt and pepper.
Oil the grill grate. Place kebabs on the grill, close the lid, and cook for 6 minutes, turning every 2 minutes. Meanwhile, warm the pita on the grill for 1-2 minutes until heated through.
Serve kebabs with warm pita and lettuce leaves, drizzling dressing over everything.