If you’re going to put in recliners you have to remove it anyway.
Unfortunately it’s paper covered press board so I don’t think it’s worth trying to repair it. But it is easy to remove, I’d use it for a pattern to make one out of real wood. Stain it and give it a few coats of good clear finish so you won’t have to worry about cup marks anymore. If you’re not a woodworker, maybe a friend or relative? It would be better than a new one.