Line a baking sheet with parchment paper. Set aside.
In a large bowl, mix together all of the ingredients except for the phyllo shells. That's the chicken, grapes, almonds, curry powder, mayonnaise, celery, salt, and pepper. Toss together with a spoon until all of the chicken is fully coated with the seasoning and all ingredients are well-combined.
Scoop a heaping tablespoonful of the curry chicken mixture into each phyllo cup.
Bake at 350°F for 5 to 8 minutes, just until the centers of the curry chicken mixture are heated through.
Notes
Reheating: If you have leftovers and want to reheat them, I recommend doing so in an air fryer or the oven. Reheating in a microwave can make the phyllo cups soggy.