Steven Universe Theory
SPOILER WARNING!
What if Pink Diamond can resurrect the broken shards of gems? Steven used this ability on Lars when he died, and all of Steven's abilities were used on both human and gems (fusion, entering minds, etc). I wonder if the ability to reincarnate was passed through Pink's gemstone? If Pink did have this ability, then that might explain Pink Pearl. The healing process may leave scars.
This would have to mean Pink Pearl would have been shattered, and, whether purposely or on accident, Pink healed the shattered gemstone. But, when Pink Pearl reformed, she had a permanent scar on her face from the damage of the gemstone. If you're still on the idea that "the gem is a projection of light and damage to the gemstone wouldn't affect it", then you're wrong - and that's not just my opinion. In the episode "An Indirect Kiss," Amythest cracks her gemstone, and it physically affecta the way her gem projected the light.
Imagine a computer. If you smash it with a hammer, it will not function correctly. If you take it apart and put it back together again, you are bound to make errors. This is what I think happened to Pink Pearl. She was taken apart - shattered - then put back together again - healed by Pink. However, in the process, the gem couldn't lock completely back into place, and, like a computer, left a scar on Pink Pearl's physical projection.