I think that part, along with the attached rubber helps with keeping the rear of the seat a little cooler (a little bit of air flow between the stock muffler and seat). Perhaps, keep heat off the plastic bottom of the seat(melting).
The rubber part, I believe sticks out some to keep crap (road grime, water, etc), from getting up inside under the seat and away from electrics.
Yamaha wouldn't have put it there for no reason...
*I took a small section of 2" "header wrap" and made a small rectangle (and sealed with A/C reflective tape to keep from un-raveling) to place underneath there for further heat protection for the passenger. Kinda moot now as the OEM muffler is long gone and the Scorps currently there have plenty of air flow around them VS the stock "heat sink"