I really have no idea why this is happening, because Banks are the only sources that accept torn banknotes.
(Is it because probably it's fake) Have you checked it?
In Greece we return every single torn note to the Banks, and it is accepted.
If by the way you take them a fake note that you might perhaps had no idea that you had such paper on you, you surely get into trouble!!!
They might not believe you, and even if you had one you would not dare take it to them.
JUST imagine having just a single $ 100 bank note which is torn, and you are in a foreign country......!
I will wait and see what other TPmember tell you though! http://www.travelpod.com/members/greekcypriot