Toss the chicken with the lemon juice, curry powder, pumpkin pie spice, 1 tablespoon olive oil, 1 grated garlic clove, 1 1/4 teaspoons salt and 1/4 teaspoon black pepper.
Heat a large nonstick skillet over medium heat. Warm up the pita rounds on the skillet on one side only, about 10 to 15 seconds. Wrap the stacked pita rounds in aluminum foil to keep warm. Wipe out the pan.
Add the remaining tablespoon of olive oil to the skillet and increase the heat to medium-high. When the oil is just about to smoke, add the chicken and spread out in a shallow layer in the pan. Turn the heat up as high as it will go. Don't stir the chicken; allow it to develop some nice golden brown color on one side, about 4 minutes. Give the chicken a quick stir and cook for another 2 minutes to develop more color. Transfer to a bowl. Taste for seasoning and add more salt, if necessary.
Mix together the mayonnaise, hummus and remaining grated garlic clove in a small bowl.
Assemble the wraps: Have 6 sheets of aluminum foil or parchment paper ready. On a pita round, smear about 2 tablespoons of garlic mayonnaise hummus sauce along the middle, then top with a scant 1/2 cup chicken, a pickle spear, diced tomato, shredded lettuce, and hot sauce, if using. Roll the pita tightly around the filling. Wrap with foil to hold the roll together. Repeat with the remaining pitas.
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