To make scratches go away? Nothing...except for a new screen.
To try to stop new ones, look at film based screen protectors rather than tempered glass. The one from LiQuidSkin seems good for some of my family members who have the Z2 Force. However, any film protector at this point may also make existing scratches stand out more...you'll have to test to see if this is acceptable.
Your screen is already shatterproof, so tempered glass is not really needed. Also, properly applied film protectors will hug the laminate plastic front screen better.
A few warnings...you really MUST watch the installation video from the manufacturer for a film based screen protector before applying...heck, you probably want to do that before even BUYING one, and more than once for good measure to make sure you have the procedure down. Watch the video on a separate device from the phone you will be installing it on, as your phone will be off during the installation procedure. If you don't have a 2nd device to do this on, make your own installation checklist for each step from the video on paper. Another warning...you are supposed to let the film set for 12 to 24 hours after installation, so plan appropriately to not have use of your phone for that long.
Also, note the position of all the sensors and microphone hole (tiny) on the front screen...when you lay down the screen protector, DO NOT cover any of these up, ESPECIALLY the mic pickup. You will be able to slide the protector into position slightly to align it. Be ready with a dry paper towel to suck up excess moisture, especially around the mic pickup once you have properly installed the film.
And again...remember to leave your phone off for close to 24 hours....this is mostly so any excess moisture can dry off.
A question/response entry for the LiQuidSkin screen protector on Amazon at one point mistakenly listed each box comes with three films...it comes with one, not three.