All depends on what the 'felt' is made from.
If NOT a 'natural fiber' such as cotton, wool, etc. than the probable best agent for removal will be a strong caustic detergent, such as a sodium silicate based detergent (commercial product called Tuff-eNuff ... available through most boat chandleries), TriSodiumPhosphate (TSP) or old fashioned 'lye soap' (Agway or 'farm animal supply'). Caustics will dissolve the mold/mildew cells. You can extract the detergent and followup rinse with a wet vac.
Chlorine based 'bleaches' will only kill the mold ... although you may have 'color shadows' remaining from the caustic extraction and you may bleach out the 'felting' with any bleach. I wouldnt go 'straight for chlorine/clorox' as a first choice but only as a 'last resort'. Products like "Tile-X" are less aggressive vs. bleaching.
With 'bleaches' you only kill the mold/mildew, and the remaining cell debris often becomes the 'nutrient source' for other species of mold/mildew, etc. So, if you choose the 'bleach route' you may have to soak with common detergent to help 'lift' out the dead cells, followed by wet vac. extraction.
Caution: do NOT attempt to remove any mold/mildew when its 'dry' ... you'll only spread the 'spores', including into your lungs - bad idea.
If the 'felt' is a 'natural' material, expect the mold to continuously 'bloom' and reoccur even after cleaning and extractions as the 'filaments' of mold/mildew deeply penetrate into the cellulose, etc. fibers.