I read somewhere that this product is very good for Plastic Do. Btw Let me inform you that I have practiced kendo for well over a decade and half. I have run Kendo Dojos and seen all kinds of kendo equipment. Bamboo, lacquer on Do's are very very rare, prized and well taken care of.
Chances are that your Do is plastic. What you can do is try this sort of novus polish or rubbing compound on the inside of the do in a square centimeter area and see how it removes similar scratches. If you do not have scratches, try adding a couple of minor ones, inside, and if it cleans it up, try adding this treatment on the problem area in minute amounts.
You can also try chatting up any of the kendo bogu manufacturer's in the western world and see if they will advise you about it.
Btw I live in South Asia and do not have access to the product below, but If I had, I would have tried it, I have a lot of donated equipment from Japan for the educate kendo cause, that I would like to bring a shine to.
I read somewhere that this product is very good for Plastic Do. But its an internet suggestion, I would only try it if I was really desperate.
https://www.novuspolish.com/
Here's an endorsement that sounds pretty convincing to me but I am not a detailer so I am guessing here.
https://www.carwindshields.info/saving-the-day-with-car-scratch-removers