Possible Clues:

• . . . hospital's eyeing poor cleanliness
• Sanitary science
• Cleanliness aimed at maintaining health
• That's a healthy way to greet a girl, by the sound of it
• Sanitary practices conducive to health
• The practice of conditions of cleanliness
• The practice of cleanliness
• 'Greet the girl, but keep it clean (7)'
• Hullo, sound, healthy girl!
• Greeting girl's reported -- this should keep things clean?