Preheat grill to medium-high. Squeeze excess moisture from spinach. Combine the spinach with turkey, feta, garlic powder, oregano, salt and pepper in a medium bowl; mix well. Form into four 4-inch patties. Oil the grill rack (see Tip). Grill the patties until cooked through and no longer pink in the center, 4 to 6 minutes per side. (An instant-read thermometer inserted in the center should register 165 degrees F.) Assemble the burgers on the buns, topping each with 1 tablespoon tzatziki, 3 cucumber slices and 2 onion rings.