Things you’ll need:
• Plastic polish
• Microfiber cloth

These items can be obtained at your auto parts store.

Put a drop of plastic polish on your scratched brick.

Rub polish vigorously into plastic. It will take quite a bit of rubbing. The more you rub, the shinier the result you’ll get.

If you’re not happy with the results, repeat the process. Note this process will remove minor scratches and shine up your bricks. This will not fix deep gouges. The picture below shows the results of having polished one half of a brick for a couple minutes. Bottom picture of before polishing for comparison.

If you have heavier scratches, you can get a micromesh kit online or at a hobby shop. This kit contains several pads and a microfiber cloth. The pads are color coded for their abrasive density. They’re similar to extremely fine sandpaper. You start with a coarse pad and gradually work your way through all the pads until you get to the finest one. Then finish with the plastic polish and the cloth as above. Below a picture of my heavily used kit.