I use tomato paste from a tube and from a can. I'm well aware of the canned anything issue but we do not use paste that often so if I find a good brand on sale I'll purchase it to have on hand. When I was younger I'd use a mini spatula or knife to remove the paste and grandpa showed me this method.
Just open both ends with a can opener, making sure the cut goes completely around. Push one end all the way through and just about every bit will come out, with little waste left inside.