Possible Clues:

• Kept part of a ticket
• The end of the cigarette? Objections may be raised
• What's left after the ticket is gone
• Residue of cigarette or cheque
• Butt - counterfoil
• It's ripped at the movies
• Butt of pencil or cigarette
• Last bit of payment in advance? What's left of cheque?
• The butt of a pencil
• Check remainder