We put down a jute rug in our dining room when we moved in and never thought about it again.

Now we noticed residue in a grid under the rug. Any ideas on what to use to clean it? I tried dry and damp scrubbing with a scotch pad, but that isn't doable. They're scraped red oak hardwood finished with what I think was a penetrating stain. Don't recall if Varathane or Minwax, but it was a blend of Jacobean and Ebony if that matters at all.

Any cleaning products that won't discolor the wood, or am I hosed?