Preheat a grill to medium. In a small bowl, mix together the yogurt, mayonnaise, horseradish and garlic.
Lightly brush EVOO on the onions. Place them, rings intact, on the grill (if you have a grill topper, use it here). Season with salt and pepper, cover the grill and cook, carefully turning once, until softened and lightly charred, about 5 minutes; transfer to a bowl.
Pat the beef dry and brush with EVOO; season with salt and pepper. Grill for 2 to 3 minutes per side for medium-rare. Transfer to a cutting board and let rest for 5 minutes before thinly slicing crosswise.
Grill the pitas, turning once, until just warmed through but not crisp, about 1 minute. Slice off the top third of each pita and spread the insides with 2 generous tsp. of horseradish sauce, then stuff with the spinach, sliced meat and grilled onions. Finish with a dollop of the remaining sauce and serve immediately.