Marinate the chicken. Combine the yogurt with minced ginger, garlic, cumin, coriander, salt, pepper, cayenne, and turmeric. Add the marinade to the chicken, mixing to fully coat the chicken. Let sit for at least 1 hour or overnight.
Meanwhile, make the garlic aioli. Combine the mayonnaise with 3 minced garlic cloves, the juice of ½ lemon, salt, and pepper. Let sit for at least 30 minutes.
Heat 1 tablespoon oil in a saute pan over medium heat. Add the chicken and cook until browned and the juices run clear, about 6-7 minutes. Remove the chicken and wipe the pan clean.
Heat the remaining 1 tablespoon oil in the pan. Saute the garlic and jalapeno until aromatic, about 1 minute. Add the tomato sauce, paprika, cumin, and garam masala. Bring the sauce to a simmer, reduce heat to low and continue to cook for 10 minutes.
Add the coconut cream and simmer another 5 minutes. Season the sauce with salt and pepper. Reserve ¼ cup of the sauce and set aside for serving. Add the chicken back to the pan and toss to coat. Simmer for 1 more minute.
Assemble the pita wraps. Split open the pita pockets and stuff with the chicken, lettuce, cucumber, tomatoes, crumbled feta, and mint. Drizzle the garlic aioli and serve with extra aioli and tikka masala sauce on the side. Serve immediately.