Fixing metal grille on a wooden radiator enclosure
The metal mesh can usually be purchased in sheets at home improvements stores, then cut to size.  A sheet isn't very expensive (last I looked, under $30).  So, it is probably easier to just replace as opposed to taking it out and trying to cleanly remove the dent.  

More research shows they come in 3x3 sheets, and you'll want to ask for "decorative metal screening".