If you mean one of those portable ironing mats that have a foam rubber pad on the underside, I have the same problem exactly and sometimes wipe it off with a damp terry wash rag. The gunk loosens up more easily if it's still warm from the iron.
I wanted to mention that the bigger problem with using starch or even just steam on one of those pads is that if you're doing quite a bit of ironing it's not as heat proof as I once thought. I had it overlapping my biggest and best cutting mat on a table and found that it didn't protect my mat from getting a little damaged from heat. You most certainly would not want to use one of these pads on a good table. Still, I like the size and shape of it and the fact that I can roll it up to take with me. I put two layers of Insul-brite under it to increase the protection, and I no longer let it anywhere near my cutting mats.
I'm curious about people using spray starch on the little reversible mats. I have a mat like that in the most common size, which is about 13" square. I have tried it and find that it's too small and starch gets out beyond it and all over everything. The foam-backed mat is about 22" X 28".