Mix all of the marinade ingredients together in a small bowl. Place pork cubes in a plastic bag and pour in the marinade. Seal the bag and toss to coat pork evenly with the marinade, then open the bag and reseal, removing as much air as possible. Place the pork in the refrigerator for at least two hours to overnight.
Preheat a grill or grill pan over medium-high heat. While the grill is heating, thread the pork cubes onto the skewers.
Grill the pork skewers until they browned on all sides and cooked through, about 8 minutes, turning once during cooking. Remove the skewers to a plate and allow to rest for 5 minutes. While the pork rests, grill the pita until lightly browned on both sides, about 1 minute per side. Remove the pita from the grill and served topped with the pork and tzatziki.
In a small bowl, mix the yogurt, cucumber, lemon juice, garlic, mint, and dill. Season with salt and pepper to taste.