Solid Hardwood, Engineered and Laminate Flooring - Stain from Non Slip Rug mat

I had my floors refinished about a year ago. About a month later I put down a area rug and used one of those no slip mats under it. Well today I lifted the rug and notice the no slip mat left a checker board stain on my beautiful finished floors. Is there anything I can do to get to remover the stain? I tried a couple of hard wood cleaners but nothing is working. I fear it would need to be resanded to get it up. Just some info there is 3 coats of poly on the floors. and checker board stain is about 3 x 4

Rubber and plastic foam mats can discolor flooring. Sanding and refinishing would be required to remove the stain. Use approved vinyl underlayment beneath area rugs.

the mat I used is for Hard wood floors. It is polyester scrim coated with PVC

Migrating plasticizers in PVC can migrate and cause discoloration of flooring. Did the mat come with a warranty? Another thought: Curing time for floor finish may vary depending upon manufacturer, temperature and humidity in the home, and whether water-based or oil-based polyurethane was used. 30 days is typical for oil-based finish. Floor finish is not completely cured until all solvents have evaporated from the finish. It is possible that the finish was not completly cured when pad was put down.