Make the dressing: Mix the mayonnaise, lemon juice, curry powder, cumin, turmeric, cayenne pepper (if using), and black pepper in a medium bowl. Press or grate the garlic into the bowl and mix to combine. Add water to thin as desired. Season with salt to taste.
Optional: Rub the chickpeas between the layers of a kitchen or paper towel to remove the skins. This makes them easier to mash.
Partially mash the chickpeas with a fork, leaving some whole for texture. (Aim for about three-quarters mashed.)
Transfer the mashed chickpeas, celery, red onion, green onion, and cilantro to a large bowl. Add the desired amount of dressing and mix to combine.
For serving: Make curried chickpea salad sandwiches, lettuce wraps, or stuffed pita pockets. Refrigerate leftovers for 4 to 5 days.
