Inside the filter, is there just a single cartridge - a floss covered one with bits inside it?
If so, yes - you will need to cut the floss, and remove the carbon bits. This is messy - you might want to wear rubber
gloves and have some paper towels handy. That floss is what your
beneficial bacteria lives in, so don't toss it out! The other option is to cut the floss away from the plastic frame that holds it all together. You don't need the actual frame, and without it, you have more flexibility to fit other stuff into your filter with the floss.
FYI, Carbon isn't necessary on a regular basis - although it is great to use post meds, as in your situation. When you are done with meds, and have run some fresh carbon in the filter for a week, fill the space in your filter compartment with a bag of
ceramic rings and some sponge. Be sure to keep the original floss though!