The rear bumper is made up of two separate pieces. There is the outer shiny (chrome or painted) thin steel cover with plastic inserts that you can see. Underneath it is a structural heavy steel frame that bolts to the frame rails (not welded) and supports the cover. This structural member comes in two types, a lighter unit that has a hole for a tow ball in the middle under the step for light duty towing or the heavy duty unit with the 2" receiver. The cover will bolt to either frame with the only difference being the plastic insert in the middle which either has a hole beside the plate to accommodate the 7 pin trailer connector for the receiver hitch bumper or one with a cutout section over the hole for the tow ball on the standard bumper. You can't just remove the receiver hitch frame because then there will be nothing for the bumper cover to attach to. You will need either the light duty frame to use with your existing bumper cover or an entire frame and cover assembly.
I just spent the better part of day under four different 355s in the local U-pull It trying to collect all the bits including the chassis harness so I can finish upgrading my truck to the factory receiver bumper. The good news for you is that the standard bumper is very common. The receiver hitch is rare. It pains me to think of someone tossing one considering all the money, suffering (loss of skin) and risk (laying under trucks precariously perched on spare tires) I've gone through so far trying to get one and I'm still not done. Trucks are for towing, else why have one. They're not very good cars and the trunks all leak.
Hmm wonder if the v8s came with the receiver bolted and welded to the frame rails from the factory because that's how I found mine when I removed my bumper cover. I recently replaced my bumper cover with a steel primed one that I had line-x do. I was going to have the receiver line-x too but found it welded and not removable with just unbolting.