Your landlord is a bit tardy in making this claim, and luckily for you, no longer holds your deposit. You can simply ignore the bill, and chances are, the landlord will let it go. If the landlord persists, he'll have to sue you in small claims court. There, you'll point out that the deposit was returned three-plus months earlier without deductions for burn marks, which will make it very hard for the landlord to claim that the marks were caused by you.

Next time you rent an apartment, be sure to take "before" and "after" pictures when you move in and when you move out. This will put a stop to any attempt by an unscrupulous landlord to charge you for pre-existing damage or for damage that appears after you're long gone.