slate backsplash in kitchen

I have slate on the walls of my kitchen the the slate over the cooktop has some grease splatter.  It has been sealed but I cannot get the grease spots off.  If I ever do, I will put an extra coat of sealer on it and (http://maplered.com) will put something up while I cook with oily foods.

 

Please advise,

Peggy Vermillion.