The two hot legs from the inverter would get jumpered together assuming you want both legs powered by the inverter. If you can have all the circuits you want to have inverter power for on one leg and all the ones you don't want powered by the inverter on the other (such as the converter, water heater electric element, fridge if two-way) and have no 240V loads in the RV, then you can power just the one leg and leave the other disconnected (or tie it to neutral, I suppose).
The neutral to ground bond (the jumper) should definitely be removed from the output terminals. It maybe should be removed from the inverter input terminal, as well, depending on how the inverter is wired and what the maker recommends. If the inverter bonds neutral and ground for its output internally, then that jumper should be removed; likewise if it's an oddball one where tying neutral to chassis ground would cause it to let out the magic smoke.
Note that you will have a 30 second time delay when switching over to inverter power. Clocks etc. will reset themselves.
IMPORTANT EDIT: Disregard what I said about connecting the ground (now in gray type above). The ground indeed should not be switched; likewise, the jumpers remain in place and are both connected to the neutral line. I was not thinking straight when I wrote that paragraph. Mea culpa.