And once again, for the newcomers: there is no such thing as "mint damage". There's "damage", also called "post-mint damage" to emphasize that it's not a mint error, and there are mint errors and varieties - some of which can look like "damage", but they're not called that.
In this case, the issue for debate is whether that ugly gash across the reverse is a mint error (strikethrough) or merely an ugly gash caused by somebody vandalizing the coin. In this case, the evidence is clearly pointing towards the ugly gash theory.
When a sharp object like a screwdriver or knife is scraped across the surface of a coin, the furrow created by the blade pushes metal out, creating "ridges" of metal either side of the furrow. These ridges are clearly seen on your coin. With a strikethrough, there isn't any actual displacement of metal, so no such ridges are created.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis