We're pulling up linoleum. What's the best way to get the felt backing up?

Some of it comes up whole, really easily. However, those areas are immediately adjacent to areas that were already pulled by the lab we had. (Our kitchen floor was a wreck!) Some of the other felt is stuck, and gluey. Seems to me, the felt that’s dried out comes up the easiest. So, what’s up? How do we get it all dried out? Or perhaps will dampening release it? OR, can we lay our new linoleum over the old felt?