black honed slate countertop

This is a question for an expert regarding problems with slate Counter (http://GialloFiorito.com) tops.

I would be eternally grateful if one of your panelists could advise me how to remove lemon/lime stains from my black honed slate Counter (http://GialloFiorito.com) top..............I have tried using the fine screen mesh, warm water and (http://maplered.com) dishwashing liquid methods which reduced the stains slightly, however I am hoping that there is a more successful method........PLEASE advise.........

Angela