Thanks for sending additional photos. I don’t think there is any need to scrape it off. Assuming it is fungal, the white part is likely only part of it; the rest of it would be filamentous and embedded within the bark and possibly other parts of the shrub. (Sometimes fungi are in the roots.) Therefore, scraping it off wouldn’t do any good. It could also be that it is just external and growing in that area because it is the shadiest and most protected part of the shrub, especially when it has leaves. I would leave it for now and see what happens in the spring. If the branches it is on don’t leaf out or start turning brown, I would cut them out. If they look fine, it is probably just a superficial fungus that isn’t doing any harm. This page from the Missouri Botanical Garden indicates that burning bushes are susceptible to twig blight, particularly in wet soil. It is possible that is what you were seeing earlier in the season; since there is a downspout drain close to the tree, it could keep that area wetter than it would be normally. However, the yew bushes nearby look fine, and they also do not like wet soil, so it may not be a factor. If you check out the MBG page, you will also see that burning bush is listed as a noxious week in many states because it escapes cultivation and invades native areas. Therefore, if it does decline, I would suggest replacing it with something else. This page from the U. of Minnesota talks a bit more about that issue and has suggestions for potential replacements.