Tribal Nutrition Improvement Act of 2022 This bill expands access to free and reduced school meals in tribal areas. Specifically, the bill makes a child who is an enrolled member (or who has one or more parents who are enrolled members) of an Indian tribe categorically eligible for free school breakfasts or lunches. Additionally, the bill allows the Department of Agriculture (USDA) to adjust reimbursement rates for breakfasts, lunches, suppers, and supplements served in Bureau-funded schools and elementary and secondary schools on or near an Indian reservation. The bill also directs USDA to establish a pilot program to award grants to 10 tribal entities for operating and implementing the National School Lunch Program, the School Breakfast Program, the Summer Food Service Program, and the Child and Adult Care Food Program in Bureau-funded schools and elementary and secondary schools on or near an Indian reservation.