Here's a possible $15.00 fix if it works and it's OEM...I've got to imagine the strap is just like the 'older' straps that came on the gas caps before flex fuel and you could yank it off. Beats the hell out of $85+ out the door.
http://www.ebay.com/itm/09-HUMMER-H2-E85-FLEX-FUEL-YELLOW-GAS-CAP-25906063-/330560774372?pt=Motors_Car_Truck_Parts_Accessories &vxp=mtr&hash=item4cf6f520e4