In a large mixing bowl, combine the drained chickpeas, diced cucumber, halved cherry tomatoes, sliced red onion, crumbled feta cheese, sliced olives, chopped parsley, and chopped mint.
In a small bowl, whisk together the lemon juice, olive oil, dried oregano, salt, and pepper to create a dressing.
Pour the dressing over the chickpea mixture and toss gently until the ingredients are well coated.
Lay out the whole wheat or spinach wraps on a clean surface.
Spoon an equal amount of the chickpea mixture onto the center of each wrap, leaving some space at the edges for folding.
Fold the sides of the wrap inward, then roll from the bottom up to create a tight wrap.
Optionally, you can grill the wraps on a pan over medium heat for 2-3 minutes on each side until warm and slightly crispy, but this is not necessary.
Slice the wraps in half and serve immediately, or wrap them in parchment paper for a grab-and-go meal.