In a bowl, whisk together all of the steak marinade ingredients. Ad a fourth of the marinade to the steak in a shallow bowl or container. Set the rest of the marinade aside before serving. Heat a hot grill to high heat. When the grill is hot, place the steaks onto the grill and get a nice sear on the bottom side of the steak. Turn the steak to the other side and cook for only a few more minutes until you have your desired 'doneness' level (rare, medium, etc.). I like my steak to be cooked on the outside but a little pink in the center.
For the sauce, prepare all of the ingredients in a bowl and mix until combined. Keep in the fridge until ready to serve pitas.
For the veggies, slice them into thin pieces.
Once the steak is done, remove from the grill and let rest on a plate for 3-5 minutes. Right before serving, slice the steak into thin strips and place on a plate. Drizzle with the marinade and then serve the steak in the pitas with the cucumber sauce and fresh vegetables.