I don't know what to do to get the stink out but do have to share this story. At our Quilt Guild meeting, one of our members shared all of the gadgets and tools sold to us quilters.
(Now, mind you, this quilter has quilted since age 13 and has a published book----Thoroughly Modern Dresden, Anelie Belden.)
She had a cut and press board like you described and her comments were the same as you---P ---U! Several members also agreed that they had had the same experience with said ironing/cutting mat. Someone suggested that perhaps it was the glue they used??????
I know I'm not much help......