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I personally would cut the old floss off of the old plastic frame, i would dump the carbon from the floss, and i would stick the old floss in before the new cartridge.
If you make a habit of changing large amounts of tank water every week or so, you don't need to service the filters more than once every couple of weeks, if that often. By flushing a lot of pure, treated tap water through the tank weekly, the filters simply move water that's already pure. The filter system doesn't get much wear and tear.
I change half the water in my tanks every week or two and service the filters about once a month. Then, I squeeze out the media and put it all back in. I use a heavy poly fiber in my filters and you can squeeze it out several times before it starts to fall apart. At this point, you cut a new piece and loss the old stuff.