Omphalos

A painter who depicts Adam and Eve must make a theological judgment call: did they have navels? Since they were created directly, should they have a vestige of a nonexistent umbilical cord? That was the launchpad for Philip Henry Gosse's famous or infamous book. 

The resurrection of the body raises a similar question. When Jesus was raised, he retained his scars. If I acquire scars in this life, will that carry over into the world to come?

In many cases, the body completely disintegrates, so God must recreate the body from scratch. In that case there's no direct physical continuity between the original body and the new body. Rather, the new body is largely a duplicate (with certain enhancements). 

Since the scars are unnecessary, incidental accretions, will our scars be reproduced? 

Scars are a bit like landmarks and memorials. Reminders of things that happen to us in this life. A physical counterpart to memory. 

I have a couple of scars from surgery. I have a faint scar on my lower lip from when I was chopping wood and a flying splinter cut my lip. I have a scar from where my sister's dog bit me on the finger as a very young boy. I have a scar from where I accidentally cut my thumb with a butcher knife. 

These aren't traumatic memories. If I retain my scars in the world to come, that's evidence that while I now exist in the world to come, I didn't originate in the world to come. Rather, I originated in a fallen world.

It's kinda like stories about someone who travels to a parallel universe. Although he now inhabits a parallel universe, he has memories from his universe of origin. His counterpart in the parallel universe doesn't have those memories. Likewise, he might have scars from his universe of origin which he takes with him into the parallel universe. He didn't acquire them in the parallel universe. Residual traces of his origins.  

Some scars might recall a traumatic memory. Some scars might be disfiguring. In those cases, God might erase the scars.