Rolling up the mat every time you're done with the grill is really the only way, I think.
If your grill is always going to be in the same spot, maybe it doesn't matter. If you roll up the mat when you pack up the grill for the winter, maybe that would help the deck fade even out as well. Not sure, but I know I read it as a warning on several products when I was looking for a mat. It's not an issue that mattered to me for my patio stones, though.