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.
Thinner and a scrub brush in a open area or you will get high... Then go over it with Super clean and a scrub brush in an open area or you will get sick. Respirator recommended but not required . Don't do this with a lit cigarette in hand.
They make a product that dissolves the glue so you can rub it off. I think GOO-GONE or Graffiti remover will work well, (non-toxic I think also) you just have to work at it a little. I do agree with Murray though. If it doesn't smell, leave it. If you want to re-paint the floor though, yeah, I would remove all of it. I looks like a really solid floor pan too, not like what you would find here in the "Rust Belt"
I use the big 4 inch wire cup on a right angle grinder for most all such. USE safety glasses. When done apply 2 good coats of Rusteolum enamel. Done. It ain't that hard.
3M Adhesive remover will take it off but using a wire wheel will be WAY quicker. I agree with using a wire cup wheel. Make sure you don't have any loose clothing on. If that wheel grabs your shirt or the string from a hoodie, you'll be in trouble before you can even react.
I used a wire wheel in a die grinder on my Barracuda convertible. It was a PITA. Don't glue the new carpet down as they were never glued from the factory. The carpet was laid in and held in place with the sill plates, kick panels, and seats.