How old is the injury? You could use a softer bristle brush around the perimeter to remove anything that loose/flaking off but I wouldn't get too aggressive.
Nothing to do. I have a desert tortoise that was run over by a tractor pulling a disc. This injury is over 30 years old:
The white around the actual injury shown in your picture is dead bone. As the tortoise grows UNDER that dead bone, it will lift and eventually pop off. It takes a very long time.
It looks like your tortoise's injury was patched with fiberglass? If that's the case, it too will eventually pop out of the hole as the new shell grows under it.
No fiberglass. Injury is probably 2 years old. When it first happened the bone was very thin like paper. After a few months it hardened. I didn't think there was much I could do. I did see, on FB, an injured radiated. They patched the hole, drew in the growth rings and then painted the plaster(?) to match the rest of the shell. You couldn't even tell there was an injury.
I've seen fiberglass patches at the zoo. Couldn't the resin burn the tortoise as it cures? I use Fiberglass quite a lot and it gets very hot when it "sets off."