Hire an asbestos professional to sample the felt backing if the linoleum was installed before 1980. If the sample contains asbestos, have the asbestos professional remove the felt backing.
Proceed with removing the felt backing if the sample reveals the linoleum felt does not contain asbestos. Begin by laying old towels over a 2-by-2-foot section of the felt backing.
Pour hot water from a water pitcher carefully onto the towels, fully saturating them. Let the moisture from the drenched towels permeate the linoleum felt for about 45 minutes.
Remove the wet towels from the felt backing. Scrape the softened felt off the subfloor using a long-handled garden edger.
Continue removing the remaining linoleum felt backing using the previous techniques. As before, focus on just one 2-by-2-foot section at once.
Sweep up the loosened felt backing fragments using a broom. Extract moistened felt particles with a wet/dry vacuum.