How do I fix a scratched lens?

So I recently bought a new green laser pointer off ebay and it was really cool, 532 nm, 1W - perfect for the low price, was really satisfied, but today my lens got a bit dirty and it looks like i scratched it while cleaning it. I tried fixing it with toothpaste, then made a thick paste out of baking soda and water but nothing helped. This is a serious scratch and I'm not even sure If I can fix it at all, but if it's fixable, how can I do it? If it's not fixable, can I get a new lens somewhere?










Here are some images of the laser itself, the lens and the dot or whatever it has now become, hopefully that helps.

The scratch is in the center of the lens, it isn't very clear, sorry for shitty camera, it looks like a dot.

Any help/tips are appreciated.