You can use black tape for a shim or a piece cut from a pop can (blacken the edge with a Sharpie). I would always shim with metal. Those rear sights often get bent like yours is. It can be straightened with just your fingers.
Just walking on the edge of of my grave.
After you get things tightened up, consider getting rid of the rear sight. Unfortunately the receivers are no longer drilled and tapped for receiver sights. The last couple of Marlins I got I had to have drilled and tapped to mount Williams Foolproof rear sights. I also put on slightly higher square post front sights like the Brockman and XSSystems. I find that a much better setup than a brass bead and open rear sight.