This is a very good reason to not set up aquariums "out of the box". Cartridges are just a scam intended to tie you into replacing them and giving the manufacturer aftersales. A filter is just a box that can contain whatever filter media you want to put in these, and throwing away the cartridges and customising the set up is almost always the better option. Everytime you replace a cartridge you will need to recycle your aquarium, they will need replacing at some point, and you can avoid that just by custom setting up your filtration.
This is a good video on how to set up your filter in a much better way than the manufacturer tells you.
In your particular circumstance, having already cycled your aqyarium, you have a few options.
1. Remove the course pad that is impregnated with carbon, and accept that you will lose your cycle, set up the filter properly, medicate your aquarium and re-cycle the aquarium at the same time.
This would be how I would proceed. The carbon in the course pad is only going to last a month or so anyway, so you should be replacing them every few weeks. Every time you do this you will set back your cycle, so get it out of the way now.
2. Treat the ich with either aquarium salt or heat. Neither of these treatments are effected by carbon, but neither is going to be as effective as the medication. Many strains of ich are now heat and salt resistant.
Just a few notes on treating ich and a mistake many people make.
Are you 100% sure its ich? There are other diseases that look similar especially to someone inexperienced.
The ich parasite can't be treated while it's in the visible, infected stage. It's only when the parasite has left the fish and moved onto a free swimming stage when the fish appears to be healed that the parasites can be killed by your treatment. This could be several weeks later. So you need to ensure that the treatment is present for a complete lifecycle of the ich parasite. The lifecycle is temperature dependant. At room temperature it takes about 3 months for a complete lifecycle of the parasite. At typical tropical water temperature about 3 weeks. At 30c/86f about 1 week.
So ideally, as long as the fish can tolerate the higher temperature, you raise the temperature to 30f to speed up the lifecycle so you don't need to medicate for so long, and medicate the water for 4 or 5 days after the last sign of infection. If the medication is removed too quickly, it will appear that the fish has been cured, but parasites won't have been killed and your fish will just be reinfected in a few weeks time.
If you don't raise the temperature you need to have the medication in the water for several weeks.
