My bigger, sliding door style (which is the later style, I believe post '70 and therefore wrong for my car, not that I care) had some paint missing, it looked like someone had redone it once before as it had faint brush marks in it. I decided to repaint. I was looking at either sanding down the chipped areas to feather in new paint or strip. I stripped. Underneath is very highly polished steel may even be chrome. Wonder if these trays were shared with other models? Where they were perhaps left shiny?, and painted for GTs, explaining why paint seems to fail on these? Just wondering out loud. I've polished mine to the point where I think I'll leave it shiny, provided the sun doesn't catch it just right and blind me.
PS be careful with stripper, I didn't realize the door handle was plastic and the stripper melted it a bit.
I've seen shiny ones before so I can only assume other's have gone the polish route too. That or I'm thinking of the flip-ups with chrome edging.