It might be possible but require a bit of elbow grease. I would expect removal of the old backing to reveal at best only a better that stained carpet hardwood floor. Remember the previous owners covered it most likely because it was in need or repair.
If I were to attempt this I would use a stiff plastic putty knife and scrape up the black rubber pad. Then use and adhesive remover to remove the adhesive. Sentinel makes a good line of adhesive removers. I would use gloves and a rag soaked with the remover and attempt removal in this manner. You would finally need to clean the floor to remove all residues. I would recommend Bona hardwood cleaner.
Good luck.