Place grilled green onions, oil, lemon juice, and zest in a food processor and process until smooth. Add the feta and garlic and process until combined and smooth. Scrape the mixture into a bowl and garnish with the additional sliced green onions.
Heat grill to high. Brush the pitas with the remaining oil and season with salt and pepper, to taste. Grill for 1 minute per side or until lightly golden brown. Remove from the grill and cut each pita into eighths. Serve with the feta dip.