Cosmoline, I work with scrap metal every day. I guarantee you that if that rifle receiver and barrel got sent to the yard with a load of scrap, somebody would find it. Not saying there's anything wrong with throwing it away. Depending on who the person was who found it, they could do a variety of things. One of them would be call the police to say they found a gun. Then you have to have the hassle of a cop coming to ask questions in your busy day. Again, not that you did anything wrong, or have anything to be worried about, just that a cop asking questions takes valuable time out of your day.
If the thing is junk, no value other than junk, it's easier to destroy it according to ATFE procedures (chop it up) and know that it's gone forever.
I went through this with a patent-infringement Spanish revolver I found at a construction site. It was rusty, locked solid, no value, junk. I chopped it with the band saw and put it in the junk barrel.
I also had a co-worker once who made a rubber band launcher that looked surprisingly like a real gun of some sort, and somebody else who made an air-powered golf ball launcher.... During a shop cleanup, they got thrown out. We had two dumpster divers put them back on our loading dock, and one visit from the local cops about the "zip gun", before I finally put them into the band saw and chopped them up too.
If it were me, I'd lop the barrel off right at the chamber, chop the reciever into 2-3 pieces, and toss it into scrap. No need to record serial numbers or anything else. It's yours, it's trash, and off it goes. Like a lawn mower, a car engine, or any other scrap metal.