Window trim detail

Anyone know how to treat this dark trim, for instance if it should be polished and or waxed? Every time I take my car in for service the preference is to wash the car and this time this black trim came back kind of dull gray and kind of spotty. I forgot exactly what it looked like before, but I think it was darker and definitely not spotty.  Hate to be fussy but I just don't want to be throwing something on there that I shouldn't because I know some trim on cars is meant to be flat or satin.  Thanks.

Something like Meguiar's Ultimate Black Plastic Restorer will work I think, but it might become too shiny. Same happens with product to put on the sidewall of tires ... some make them just glossy black, way too much shine.

You are right, that black piece of trim is not supposed to be gloss. I looked at a photo before taking the car in (attached) and it is more of a satin appearance rather than gloss. Before using some restorer on it maybe I will try a bit of wax & see what happens. I think whatever they used to wash the car tends to strip it since the surface wasn't slick when I got it back.