Not to sound confrontational, but I don't know if that's a good idea. That plastic makes a vapor barrier, mainly keeping moisture away from your wiring and spkrs. If you're not going to recover the door with sound deadening material, I'd just peel the plastic back and go looking for your rattle. It will reseal fine if you press it back on firmly. And also, removing it would let in more dust and dirt that "plastic piece" is keeping off the spkr. You best bet is still to sound deaden. You can get 10 sq ft. of eDead v.1 dirt cheap, put it under your spkr (between it and the door's metal) and over the rest of the door creating a sound barrier as well as an enclosure. This will both remove rattles, resonance that robs your spkrs of sound quality, bass and volume, and lower the noise level on the freeway (so you can hear more of your music!). If that little plastic piece is what's rattling, put some SD on it too. Presto, rattle gone. If your spkrs are not mounted to the metal itself but to some factory plastic adapter, then SD it to, it will stiffen it and give you better bass.
Anyway, that's just my experience and opinion. Considering the meger cost and the exceptional results, it's your best way to go.