Not sure why you haven't had an answer yet but as you probably suspected you need to remove the burned wood, it's really the only way.
Slight discolouration around a burn might be bleached using oxalic acid but the main scorching and any charring needs to be physically removed. How deep are the burns, how thin in the wood?
I have used a cloth with alcohol to rub away carbon deposits, and this has worked well for me. If it’s more than carbon deposits though this isn’t going to work though, and you will have to resort to fine abrasive paper.
