The styrofoam is there for a reason. You wouldn't take it out of the front (unless you need to to fit an intercooler, for example) so dont take it from the rear. Not sure what the laws are like in your area but you're more likely to sustain more write-off worthy damage in the rear than with the same impact to the front, styrofoam or not.
That aside, a piece of styrofoam isnt going to make the rattling noise you are describing. It's so light and has a soft surface so even if it was hitting something, the sound it would create is more of a dull noise. Take the towel out, wrap all loose objects with EVA foam (cut up a camping mat or old mousemat, old wetsuit or whatever - it's the black high density foam you're after) then squash it all back together along with the styrofoam piece. The more snug everything is, the less room for objects to vibrate and cause a nuisance.
There's also a thin metal heat shield above where the stock rear muffler would sit - that can rattle like a m*therf*cker but it never rattled on my car
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