What should I do about this fixture brace?
If the brace is loose, you're going to have problems with vibrations sooner or later.  The braces that I see these days look a lot sturdier, so I'd recommend replacing it.

If you have access to a Roto-Zip (or similar tool), a metal-cutting wheel should make short work of the original brace, just cut it off near the joists so there's less to worry about.

It looks like the original brace is bowing the drywall down a little at that spot, so look into a new-work brace that can adjust for different thicknesses of drywall: just break off that tabs that allow it to be installed with 5/8" drywall because they'll interfere with the pieces of the original brace, and mount it so the edge of the box is flush with the surface of the drywall.  Be careful to keep any wiring away from sharp edges you might have from cutting the old brace.

If that's not going to work, install an old-work brace in the spot; look for one with a larger junction box (the one I linked to has a 2 1/8" deep box) so that you can mount it above the original brace and still have the edge flush with the drywall.