The tire needs to rest against the rubber snubbers to keep damage from happening to your tailgate. With the bigger tire, and stock wheel backspacing/width/offset, there will not be enough room to mount it the correct way. That is why the PO put it on backwards.
Do you have aftermarket wheels on the Jeep? Do you plan on running the stock wheel/wheels for awhile?
If you have aftermarket wheels on the Jeep, you could get a matching wheel for the spare. Or, if you plan on running stock wheels, you could remove and cut down the rubber tire bumpers to make more room for the 31" tire. Or, you could get a aftermarket tire carrier or bumper/carrier combo.
Hope that helps.