If you have grease on your G-10 handle just wash it good with Dawn dish soap. Remember the commercials? - "Dawn... gets grease out of your way". Really, it removes oil, grease, fat, etc. pretty quick. If it is just grease, it will come off.
Now if your handle is discolored, don't know what to tell ya! I have never used Militec, so I don't know what it's like. The 3 things I use on my knives are Break Free, 3 in 1 oil, and Tuff Cloth. None of those products have ever stained my knives (including G-10). If you are having bad luck with Militec, you might want to switch to something else. By the way, those stains on your knife... they're called "character"! All using knives get 'em! When a knife (that I intend to use) gets stained or scratched, it just makes it more "mine".
Your BM 806 is a fine tool. If you intend to keep and use it, I wouldn't worry about a mark or stain here and there. Just look at them as character marks that come with use and enjoy the knife! It's what you shelled out your hard-earned money for. If you intend to trade it sometime down the road, baby it. If it's a keeper, use it and don't worry about a stain here or there.