What you're seeing is partially oxidised grease, whilst it doesn't actually ignite, the heat still allows the unsaturated oils to oxidise to some degree. The fun thing about oils is that they don't really like dissolving in polar or non-polar solvents, but a mixture of the two, some sodium hydroxide in an emulsion of water and alcohol should do fine. If not, you could use hexane or some petrochemical non-polar solvent (don't use benzene, despite the fact it'll get that stuff off with ease, everyone will get cancer).
P.s: the spent grease makes an awesome fuel, if somewhat smokey. If that's a problem, just chuck some KNO3 in it or something.