Trim tenderloins of any extra fat and silver skin. Cut into 1" to 1" cubes. Add Salt and pepper to tenderloin cubes, then let sit for 5 minutes. Place in a bowl or resealable plastic bag.
Add remaining souvlaki ingredients to bowl and mix until all cubes are coated. Cover and refrigerate for a minimum of 2 hours.
If using wood skewers, soak for 30 minutes. Light grill, and bring up to a medium hot temperature. Skewer meat and vegetables. Place on grill and cook for 8-10 minutes, rotating every 2 minutes.
Remove from grill and let rest for 5 minutes while you grill pita bread. Remove and serve with Tzatziki Sauce.