Drain and rinse chickpeas thoroughly, then place them in a mixing bowl. Use a fork to gently mash about half, leaving some whole for texture. This creates a mixture that holds together while still feeling hearty.
Add tomatoes, cucumber, red onion, olives, parsley, olive oil, and lemon juice to the bowl. Season with salt and pepper and toss gently until evenly combined. Finally, fold in crumbled feta so it stays chunky.
Lay each wrap flat and spread hummus or tzatziki if desired. Spoon the chickpea mixture across the center, fold in the sides, and roll tightly. Slice in half and serve immediately or pack for later.