The black stuff is iron particles that have been abraded from the table saw top. To remove them from your pads, you'll have to dissolve them.
The good news is, it appears that the festool cutting compounds are water-alkane emulsions, which means that you should be able to remove the majority of the residue by simple laundering with clothes detergent. I would do so by hand, and gently, given then at least one of them is made of wool.
Following that, there will probably still be some black residue remaining. Acids are the easiest way to dissolve these. Again, given the wool composition, I would go with weakest acids first - soaking in ample vinegar (acetic) or cola (phosphoric) will probably work. If those don't work, I would use dilute hydrochloric acid (commonly found as toilet bowl cleaner) - work your way up from extremely dilute to more concentrated. Following the acid treatment, launder again in multiple washes of plain water. Remember to be physically gentle so as not to ruin the wool structure, and to only be as chemically harsh as you need to be, and be patient - the vinegar/cola might take a day or two of soaking.