Pull up the rug and rug gripper completely, and move them into a different location so you have full access to the marks on the floor.
Dip a sponge into a mixture of water and mild dish soap, and wash the pad marks away. It may help to have a two-sided sponge with one side used for scrubbing. This scrubbing side may help you to remove the pad marks.
Apply some extra strength glue product remover, such as Goo Gone, onto the pad marks if the soap and water didn't take care of the problem. Let the Goo Gone sit in on the marks for a few moments, and rub it in with the sponge. You should see the rug griper pad marks come right off.
Wash off any excess cleaner with a clean sponge or damp rag.
Dry up the floor thoroughly before placing the rug gripper and rug back into place.