Best backing for oriental rugs?

We have tile floors and oriental (Turkish) rugs. When we bought them about ten years ago we placed under them the backing the dealer recommended: a sort of rubberized mat, tan, with a grid of white fibers embedded in it. Recently, we sent the carpets out for cleaning.

We found the underlying mats to be somewhat deteriorated and not pleasant smelling, so we decided to replace them. Now I'm wondering if they really need to be replaced. I'm not talking about small carpets, which need something under them to keep from slipping -- these are 9 X 12 or so, and they are not going to slip. Do they really need an under-lying layer? If so, what is the best kind? Thanks.