Apple Pen Scratched iPad Pro!!

Freaking Apple pen cap scratched my iPad screen. Normally, my iPad has a screen protector. However, it was bubbling so I took it off and ordered a new one. Of course in the interim of one day I was walking around with the iPad in a felt case with my Apple pen and the **** pen cap fell off and scratched the iPad screen. Some of the scratches are hidden by the new screen protector, but several deep ones are noticeable under bright or white back grounds.

I can't stand defects or scratches and this is a device I use regularly for work and will use for years to come. I didn't realize the pen cap would come off so easily and the iPad pro screen is supposed to be really durable. So, needless to say I was pretty shocked. I've already contacted Apple to see if they would replace the screen, but of course that's a no without paying the $599.00 replacement fee. Screw that. I've already paid $900 for the iPad and another $100 for their **** pen (it's actually an awesome stylist but the pen cap is a serious defect.)

I would like to fill in the scratches but can't find anything online to that affect. Has anyone tried this and what product did you use? I don't want to "buff" them out, but "fill" them in. There must be some product that can fill in or minimize the deeper scratches?

PS. Yes, I've tried toothpaste. No, it doesn't work.