IMO scars are part of your life's journey whether they were caused by an accident, physical illness requiring surgery or mental illness. I really see no reason why you should be obligated to cover any scar (or birthmark as the other answer suggested).
Many people have physical characteristics that may be distracting whether it's an enormous nose, squeaky voice, pock marks all over their face, 200 pounds of extra fat, or a woman with excessive facial hair. If the guests are unable to focus on celebrating the couple because they're so easily distracted by physical appearances, then they need to get out more.
I truly believe if you have mentally healed and are healthy, you have no reason you should be embarrassed or feel obligated to hide your scars. As I said, they are part of your life's journey and were a stepping stone to who you are today.