TAPP Water refill cartridges are entirely made out of non-toxic materials which remain inert after decomposing. The cartridges contain a high percentage of biodegradable and compostable material and can be disposed of with organic waste. This organic waste ends up in an industrial composting plant where the cartridge breaks down within 1-2 months. Alternatively, it can be discarded with general waste, where it will break down within a couple of years in a landfill or be burned without causing any plastic residue. It will also take a couple of years to break down in a garden compost, so not recommended.
Note, that the device itself (without the refills) is made out of highly recyclable ABS polymers, and can be disposed of with plastic waste.