If you can make it go away by wetting it, to me sounds like it is in the clear coat. You can probably get away with wet sanding it or using something mild like some kind of gritty polish. The only real problem is if it is just in the clear and you can polish it out you are thinning the clear so it is susceptible to doing it again, but you may get away with it.
Here is what I would do if I were you,
I would wash it and see if water makes it disappear, what ever you still see will not be fixable as it is in your paint. If you can make it all disappear you are golden. Then while it is wet I would clay bar it as smooth as you can get it. Then wax it here is what I use for wax.
https://www.amazon.com/gp/product/B000AP8DZY/?tag=wranglerorg-20 this is mildly abrasive and actually if it was me I would wet sand it, but you could do damage if you don't do it right, so I would use the polish; it will take a lot to hurt it. Then after dried I would wax it again with this to protect it if it worked.
https://www.amazon.com/gp/product/B004HCS4PK/?tag=wranglerorg-20
That should at the very least make it less noticeable. Don't do any off this till you talk to your insurance company first though, because if they do decide to repaint it and clear it that will give you the best protection in the end assuming they do it good and right.
Sorry to see that on the perdy red tj!