Divide meat into four portions and form into half-moon-shapedpatties to fit on half a pita bread.
Use a fork to mash the garlic with butter in small bowl; set aside.
Heat olive oil in skillet over medium-high heat.
Add mushrooms, onion, salt and pepper; cook until tender, about 5 minutes.
Prepare a charcoal or gas grill for cooking.
Spray grill rack withnon-stick cooking spray.
Cook patties to desired doneness.
(Can be done in a covered grill. For medium rare, cook about 4 minutes on one side; turn and cook 4 minutes more.) During the last few minutes of cooking, brush one side of each pita with the garlic butter and place, buttered side down, on the outer edges of the grill to toast lightly.
Place a pita, toasted side up, on a serving plate.
Place a patty on one half.
Top patty with 1 tablespoon feta cheese.
Place part of the mushroom mixture on the other half of pita.