Sorry to hear about the guppy. It sounds as though there were more problems than just the whitespot. A lot of experienced fishkeepers will not keep guppies because of them dying, an all too common problem nowadays. Yours could well have been one of these weaker fish.
If one fish had whitespot, the whole tank is infected so you need to continue the treatment. The half of the old carbon filter still in the filter, in theory, will remove the med but in pratice if it's been there more than a couple of weeks it should be 'full' and not remove any med.
Because all you have in the filter is half the old carbon filter and half a new sponge, you need to be very careful about what you do next. The remains of the carbon media will contain half the bacteria you had. But you now only have half the fish you had, so that should be enough bacteria. Don't touch the remaining part of the carbon media. You need to wait until you've grown some bacteria in the new sponge before you touch the carbon. That will take at least 4 weeks, maybe six.
Leave the filter alone (apart from a light clean in old tank water that you take out during a water change). In a couple of months, take out the last bit of carbon media and put more sponge in its place. Then you'll have just 2 bits of sponge, which is good.
Forget what I said about using some new carbon to get rid of the med when the treatment is over - that's only for when you have some other mature media in the filter which you don't have. You can remove the med by doing more water changes - you'll be doing those anyway if you find any ammonia or nitrite in the water.
I've googled your filter but the manufacturer's website doesn't appear to have the manuals. (Some do have manuals available as downloads, which is very useful for someone like me to find out about other people's filters
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