That's an 03/04 bumper. Usually that part is a flat black. I don't think you can really polish.Hard to tell in this photo if this is a oem New Edge Cobra rear Bumper (the Cobra lettering seems way to big) and what ever those streaks are if they cant be wet sanded, cut and buffed or polished out than you need a repaint and/or new bumper.
Looks like some type of chemical contamination that etched into the valance. I sent @NastyGT500 (Scott) a text and asked him to check out your thread when he gets a chance. He's a professional detailer, and a great one, so hopefully he'll be able to help you out if the issue is fixable. I've personally never seen streaks like that before.
The streaks don't appear anywhere else on your car? How about the lower side skirts?
Nothing was 'on top' of those streaks/marks? Just the stains?
Very strange, looks like some type of liquid or something was on there, dried and left a residue behind. First thing that came to mind is hard water stains from a sprinkler, but that would have been on additional areas of the car.
What have your tried to polish off? What product and what method?
I see that it is black plastic, it may be susceptible to 'high spots/bright spots/shiny spots' if you polish it. See how it reacts/responds.
As of now I would lightly machine polish and see your results.
You could also soak the area with an all purpose cleaner, let it dwell, and see if that removes any of it.
Then wipe it down with a paint prep/diluted IPA mixture.
I would then treat the area with a trim restorer product afterwards.
You can also ceramic coat over some of the products and call it a day (or two).
Hope this helps, let me know if I can be of any other assistance, and if you can post up some close up/zoom shots of those spots.
Regards,
Scott
Keep us posted. Thanks to @NastyGT500 and @311-420 for their input.