Place the cucumbers in a medium bowl and toss with the red pepper, 1 of the finely chopped garlic cloves, and ¼ teaspoon of the salt. Toss to coat and let stand for 15 minutes. Stir in the parsley.
Meanwhile, combine the pork, oregano, thyme, black pepper, the remaining ¾ teaspoon of salt, and the remaining garlic in a large bowl and mix well. Divide into 4 equal pieces and form into ½-inch-thick burgers. Heat the oil in a large cast-iron skillet. Add the burgers and cook over medium, turning once, until golden and cooked through, about 8 minutes.
Slice the top ⅓ off each pita and spread the yogurt inside the pocket. Stuff with the burgers, onion, and salted cucumbers. Serve warm.
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