Toss together cucumbers and 3 tsp. salt; drain cucumber mixture in a colander 30 minutes.
Meanwhile, preheat grill to 350° to 400° (medium-high) heat. Brush onions with olive oil, and sprinkle with remaining 1 tsp. salt. Grill onions 3 to 4 minutes on each side or until charred and tender. Cool 10 minutes.
Stir together cucumbers, onions, garlic, and remaining ingredients. Let stand 30 minutes.