I too think the plastic thingy could be amplifying the noise. But here's what ya' do: First, make sure the pads are correct, and properly seated. Second, make sure the disc is centered and bolted properly to the wheel. Third, check to make sure there are no loose spokes, or cracks in the rim or hub( this is a wheel integrity check for step four). Four, bed in the pads. Get the bike going fairly fast, preferably downhill, and apply the brake (don't skid that tyre it won't help), do this maybe 5 times, yes the disc will get hot ,don't touch ! Let it cool down and then repeat your noise check.
The reason bedding in works to reduce noise is because the former pads would have worn with the disc and so heavy application of the brake puts those same grooves into the new pads. A slight flat sanding(800 grit) of the disc could act as a brake lathe does to restore the smooth finish to the disc. This said I don't even have the discs on my car turned anymore because it's so cheap to buy a new set, likewise a standard 6 bolt brake rotor for a bicycle isn't too much to replace.