Yet another cork question -- how do I clean cork tile?

Hello Eichler people,

I now have exposed original 1954 cork tile in the LR and DR. And it's kinda' gritty in some areas? What can I do to clean this cork to restore it to its original luster before I apply the poly-whatever it is?

All the cleaners I've read say "wood, wood, wood" but "cork, cork, cork." Right now I plan to use Murphy Oil Soap.

What do you recommend?

Thanks.

David