You should be able to just remove the hinge pin and not have to grind, but if you want the stock luggage rack gone, as it is not for bikes, not 4 bikes, then you can cut it off.
I'm not here to ask why the rack cannot be just removed. He said it is welded on, I provide how to un-weld it. Welding is not as permanent as the grinder is.
After you get a proper bike rack you will say, this was such a good move.
**edit to below... ALL hinges are removable with a grinder! Damage to a pin can be undone with a bolt. If OP wants a bike rack and has a luggage rack, and if luggage rack is in the way then he needs luggage rack gone to make room for a bike rack. Carrying 4 bikes is a lot different than strapping one or two on a luggage rack. A real and well made bike rack is really the best option.
The 1UP is still a great choice for this location, but it is expensive too.