I have stair handrails held on by brackets like the one in the image. The bend in the loop piece has a larger diameter than the diameter of the post on the bracket that it loops around. Also the post on the bracket sticks out a bit longer than the loop. These two things lead to a little bit of play back and forth in the directions indicated by the arrows. So the handrail can wobble back and forth about a quarter inch or so.
Looking around online for a solution it seems most everything is just assuming there are screw(s) loose somewhere that need to be tightened.
I've double checked every screw on both the wall bracket side, and the handrail loop side and all of the screws seem to be fastened securely.
Is there a "correct" way to tighten up the loop so that it grabs the bracket post more securely to prevent the handrail from moving at all?
My first inclination is to use some sort of filler, perhaps a little piece of cardboard or something wrapped around the bracket post to make it a little bit bigger so that the loop will fit more snugly to prevent the movement. Are there any reasons why that is a bad plan?