'68 Barracuda carpet pad/glue removal tips

I don't remember Mouse Piss being a carpet color in 69. LOL
Like @Murray suggested, you don't really need to remove it, unless it is soaked with urine odor.
If it is not, I would just hit it add with a DA sander with 80 grit. That will get rid the loose stuff. Then vacuum thoroughly. If it is soaked with the urine smell. I would sand it MORE with the 80 grit on a DA sander to get off what I could, Then I would switch over to a 3" Roloc Disk on a 90 degree die grinder. That will get it all off; all the paint too. You will have to protect the areas that got down to bare metal.