Season burgers with salt and pepper. Grill to your preferred temperature.
In a small bowl, combine garlic, lemon zest, lemon juice, oregano, salt, pepper, and basil. Gently fold in tomatoes, green onion, and feta. Transfer to a bowl and garnish with more basil if desired.
Add burgers to pita, top with a generous helping of hummus, tomato and feta dip, and fresh basil.