Preheat your grill over medium to medium-high heat.
Grind the venison and pork using your grinder's small die.
Add the garlic, onion, parsley and seasonings to the meat. Mix well until incorporated. Now is a good time to cook off a small bite in a pan and check the seasoning for taste.
Cut the pitas in half and stuff them with enough meat mixture so that when you flatten the pitas, they are around 1/4" to 1/2" thick.
Gently press them with your hands to flatten them uniformly.
Lightly brush the pitas on each side with olive oil.
Place them on your grill and cook for about 5 minutes, ensuring that they don't burn.
Flip the pitas over and move them to a cooler spot on your grill. Close the lid and cook for another 5 to 7 minutes.