I like this coin but does the back damage take away the value? And what cause the damage on the back?
It looks like there may have been a sticker of some sort there at one point. Can you rub this off with your finger? Value depends on demand. This is a nice off center error but they are actually worth more if you can find them with dates.
Maybe a Ferrero Rocher sticker?.. Seriously it's not that bad of a "damage spot". It's still a 95% way Off Center Cent that has a nice value to it regardless of that spot.
I would leave it as is then. It's a very nice error. You can cause damage to it if you try to clean it. I have plenty of Off-Center Cents with spots like your Cent.
Just leave it alone. It's a blank planchet that bounced out of the chamber when the dies tried to come together on it, and they only got that small piece of it you see. We don't have any handy-dandy price guide that will tell us what its fair market value is, so you want to research that issue, looking for comparables, and try to set your price off those. That's a very sweet error, a very nice one.