If the oil used is mainly mineral oil-based, I'd first just wash the knife in tolerably hot water (~120°F) and liquid dish detergent, like Dawn, Ivory, etc., scrubbing the stained areas in particular. This usually does a good job with light mineral oil in general. I'd avoid things like brake cleaner & acetone, which can be too harsh on some materials, like adhesives used to attach the bone scales and shield (CA 'super' glue and/or epoxy). If the soap & water wash doesn't quite handle it, some mineral spirits would likely do the next-best job in thinning out the oil for cleaning it up. I'd follow that again with the dish soap & hot water. But, I've seldom had any troubles cleaning up mineral oil-based products with just the dish soap & hot water alone. After washing, rinse the knife in hot water, which warms it up and therefore helps to evaporate off any residual moisture. Then carefully re-lube the knife as needed.
If the staining is just a slight darkening or 'warming' of the light-colored bone, without any staining from dirt or grime, you could also just lightly wipe down the whole handle with the oil, to even it out. With light mineral oil, if just applied very lightly and infrequently (no more than 2 or 3 times a year), you'll essentially see no trace of it after a few days or weeks.
David