This is something new on a turtle you gave had for a while? You say it feels like gum and to me it looks like it is on top of the shell. My guess is a fungus, or...dried up gum.
I think Yvonne is right - looks like the outer layer of the carapace has been damaged, revealing the bone below. I usually see this in box turtles that have had an encounter with a dog or some other chewing animal. I would be interested to see if there is damage on the plastron below, since this looks like upper jaw damage - curved to fit a dog's snout..
Here is a closer picture I took this morning.
I was given this turtle as is so not sure how it got these markings
Fungus is interesting - is there a way I could tell and or remove it if that were it?
Also - if it is shell damage .. is there something I should do or just leave it be?
I agree with shell damage and does look a lot like animal bite. Personally would suggest some antifungicidal ointment be kept on it for a couple months and before hibernation if you hibernate. Should not be a problem once body has compartmentalized the damage.