Screening With Dignity Act This bill directs the Transportation Security Administration (TSA) to develop procedures to appropriately and respectfully screen self-identified transgender air passengers and passengers traveling with religious headwear or other articles of faith and begin training of all TSA Officers on such procedures. The TSA must implement protections for such passengers, including (1) prohibiting human viewing of passenger images and conducting pat downs by an officer of the gender requested by the passenger; and (2) ensuring secondary screening measures are no more intrusive than necessary to resolve an alarm or other concern raised by primary screening, including consideration of the sensitivity of the groin, chest, and other body areas and the sensitivity of religious articles of faith such as religious headwear. The TSA shall separately study and report on (1) the cost and feasibility of retrofitting advanced image technology screening equipment to distinguish between foreign objects and human body parts (including hair) in a manner that is gender neutral; and (2) the impact of imaging technology on transgender passengers, passengers whose religious faith requires them to travel with articles of faith, and passengers traveling with assistive devices. Additionally, the TSA must identify any policy, procedure, or training changes and complete any testing, certification, and assessment for qualifying additional technology to ensure that any advanced imaging utilized for passenger screening meets certain requirements, including not generating alarms based only on passengers' body parts (including hair), undergarments, or religious headwear.