In a 1-cup liquid measuring cup, whisk the 1/2 cup oil with the ginger, Tabasco, vinegar, garlic, 1/4 tsp. kosher salt, and 1/4 tsp. pepper.
Thread four cubes of meat onto each skewer, inserting a red pepper square between the cubes. (You may not need all the skewers.) Brush the kebabs with oil and sprinkle lightly with salt and pepper.
Just before grilling, lightly oil the grill grates. Set the kebabs on the grill and cook, with the lid closed, turning every 2 min., 4 to 6 min. total for medium rare. Warm the pitas on the grill.
To serve, slide each kebab off its skewer into a pita. Top each with some of the lettuce. Whisk the dressing to recombine and drizzle over the meat and vegetables.