It is best not to use carbon with live plants since it can remove some of the nutrients, however, once the carbon is used up-usually in about 3-4 weeks depending of the amount/quality of the carbon itself-you can either leave it or remove it all together-either way is fine....
If the filter media is the combined type...sponge with the carbon all in one piece-you can cut a small slit in the sponge and dump the carbon out and keep the sponge in the filter or just leave the carbon-it won't hurt and it will provide more surface area for good bacteria to colonize on.....
I would remove the filter cartridge a couple of times a month and give it a good swish/rinse in the bucket of old tank water with a water change to get the big pieces of gunk off to help maintain good water flow for the good bacteria-its sticky and adheres to everything so you won't wash it off-but chlorinated water can kill it and why you want to use dechlorinated water or old tank water......