Drain and rinse the chickpeas well, then pat them dry with a clean towel so the bowls don't turn watery.
Whisk the olive oil, lemon juice, garlic, oregano, salt, and pepper in a small bowl until smooth.
Dice the cucumber, halve the tomatoes, slice the red onion, and chop the parsley.
In a large bowl, combine the chickpeas, cucumber, tomatoes, onion, olives, and parsley.
Divide the greens among 4 glass containers. Spoon the chickpea mixture on top.
Add the feta, if using. Pour the dressing into 4 small leak-proof containers.
Seal everything and refrigerate. Add the dressing and avocado right before eating.