Lots of elbow grease and a mild abrasive, like Bon Ami. Stinks, I know. I'm in love with my Silpat, but I also just love parchment paper, and it's saving my pans.
"In all our woods there is not a tree so hard to kill as the buckeye. The deepest girdling does not deaden it, and even after it is cut down and worked up into the side of a cabin it will send out young branches, denoting to all the world that Buckeyes are not easily conquered, and could with difficulty be destroyed." - Daniel Drake, 1833