I wish I could tell you how to remove the sticky stuff, but alas put a claim in with the mover and let them pay for new mats. Working for a mover for over 10 years I can say they will probably pay you for it, get an add with what you want replaced and include with a letter to the claims department.
When we moved they lost our patio table, I filed claim and sent the receipt in for my purchase that I found on sale at a great price. I received my check almost in return mail, they really do want satisfied customers when all is said and done.