I would say that you are the best person to answer this question. If the secondary filter IS getting dirty, then that is 'stuff' which the main filter doesn't have to deal with. If it's a hassle to have the extra filter, you could try putting it in place only for the first week after a water change, or after somebody like my brother in law:
uses your tub, and then storing it the rest of the time.
Your dealer may have some insight - if there are local water issues which make it a good idea to use this thing, or perhaps not worth the bother.
HTH