Like Norty, ours was factory installed and is not through bolted. I had it off a few weeks ago so I could replace the foam handle, and the screws that hold it in are a heavy gauge at least a #10, maybe #12? They are certainly biting into something very solid behind; I would say it was metal rather than wood structure based on the tightness of the screw all the way out, but mine is aluminum framed. That leads me to also believe that there is a "sweet spot" for the mount, at least on models that offer it as an option (was standard equipment for our model year). Add a bit of butyl tape behind to keep things dry.
One question to OP, when you say it is loose, do you mean the mounts on the wall are loose, or that the handle itself has become sloppy? There are two springs inside the mounts that keep the handle pulled down tight to the mounting bracket, and if one is broken it could cause looseness. My foam replacement kit included new pivots and springs as well.
2011 Jayco X19H (purchased 2015)
2008 Jayco 1007 PUP (purchased new, traded for the X19)
2012 Chev Traverse LT with TP