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If it's oils that have soaked into it you can use a number of techniques to try and dissolve the oils and then lift it out of the stone (sometimes impossible). If the surface has broken up it will depend on the type of granite. You might be able to polish it with a mixture of very fine grits (400 upwards) but it won't be easy. Resealing is required maintenance, depends on use but annually is not a bad idea.
Has anyone here ever tried restoring a pretty manky granite worksurface? Not sure if I just need to reseal it, or whether it perhaps needs grinding/heavily polishing in some peculiar way.