Restoring dented boxes

I recently bought a new ottoman bed and thought it would be a great spot to put some of my figures as I had one previously which worked a treat. Unfortunately in one particular section I misjudged how many I could stack vertically and now I have 4 or 5 boxes with dents at the back. Luckily there is no other damage or creasing.

So my question is.. Has anyone tried to restore the shape of their fig boxes and if so, what are your best methods?