Kerosene will cut the grease. Use a cloth or a stiff vegetable brush if you have to but be careful not to abraid the tiles themself any more than you have to. (The surface of tiles is glazed but underneath is just baked clay and it is not glossy.)
Then use Ajax or Comet or any scouring cleanser with high abrasive qualities and a scrub brush (the kind they used to use for cleaning floors.) Scrub with each line of grout. Rinse very well. Dry with old towels and seal with any good grout seal. (Available at most home improvement or tile stores.) The counter should be cleaned and resealed periodically.