IMO, filter cartridges are good until they start to fall apart. You don't want to replace them too often because that is where most of your good bacteria live! Just rinse it out in the water that you take out of the tank when you do your water changes, DON'T rinse it under the tap!
Oh, and once the old cartridge wears out, slip the new one in behind it (if you can) for a couple weeks before you change them out so the new one can build up some good bacteria. That way you won't stress out your Betta!
Gah...Okay. Money, money, money...
But my pets are worth it.