Use and cleaning of silicone baking mats/cookie sheets

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I bought two of these new silicone mats for baking, and they worked so good and were so easy to clean that I decided to use them for other things that usually stick to the metal cookie sheets when I cook them. So, last night I used them (on top of the regular cookie sheet) when I baked some frozen fish fillets and fries in the oven. Now, my silicone sheets have a greasy coating on them that won't wash off completely, and a couple of little scorch marks where (I think) the oil form the fish may have pooled up and cooked off. So, I'm guessing that these mats, great as they are, are only meant for baking "dry" or non-oily foods. Has anyone had a similar experience? More importantly, anyone know how to get off the oily film without harming the mats? Thanks.