The necessary passport prompt only happens at kiosk check-in for an international flight. At your next international flight, check in at an airport kiosk and pay close attention to the prompt message that appears after you scan your passport. You have to say "yes" to the question "Do you want Delta to save your passport details in your Delta profile" or words to that effect. That "yes" choice is the action that "verifies" your passport in your Delta profile.