Apparently, some users here agree there is no ion exchange through the skin. Mud therapy has some therapeutic effect for pain related diseases. As an anecdotal example, I experienced pain relief by treating my sport injury using mud therapy. If it is not ion exchange, then what is the mechanism behind mud therapy?
The answer on the linked question is apt: transdermal administration of medications or other compounds include exclusively lipophylic compounds, i.e. uncharged 'fatty' materials, such as nicotine, opiate-bases and steroids. Minerals, like those found in clay, are highly hydrophylic and are therefore unlikely to be taken up by the skin.
A search through a bunch of articles makes me believe that mud therapy has mainly a thermal effect, i.e. a mud pack heats the underlying tissue and thereby relieves muscle spasms and pain (Espejo-Antúnez et al., 2012; Liu et al., 2013).