A project that finds out someone is running slanderous campaigns about them, should first of all ignore them. Majority of these are trolls, so if they dont get any attention from their victim they will stop.
Still if they dont seem to stop, the project can give a public announcement to clear their name and then never again take any statements about it. This shows that the owners do not care about any hate campaigns but are more interested in developing their own stuff. Gradually though, as I have seen, these trolls stop and they move on to harass others. If you give them attention, they will do more of it. Ignoring them is the first step.