Possible Clues:

• It's the girl that's the thin one
• It may pop out of a box
• Delicate fabric
• It's herself that's thin
• Thin soft disposable paper
• Disposable piece of absorbent paper
• Times initially put out paper full of lies?
• Sit up and beg and dry eyes I may bring
• Paper, 'The Yorkshire Post'
• Gift box liner