agreed. that filter material is covered in beneficial bacteria for your nitrogen cycle. every time you toss it out, you lose a chunk of your bacteria. In a very heavily stocked tank, that could cause a little ammonia to appear for a short time, as the new filter media gets colonized.
This is one reason I recommend Aqua Clear filters...because yo udon't have a cartridge, but a larger foam block, which will last more than a year before needing replacement.
But essentially, no matter what HOB
filter you have, just rinse off the filter media in the tank water you drained during a water change, and keep using it. If the cartridge has carbon inside, I would cut open the corner after using it for a week, and remove/replace the carbon. Carbon is only 'active' for 7 days, then its just idle. if its a really poor grade of carbon, it could actually start to decay and leech phosphates back into your tank, which could cause algae problems.