As far as I understand it, after the 7 day period you should do a 25% water change, as per package instructions. At that point if you wish to you can put carbon in - it will help to remove any remaining medication, but in my opinion it really isn't necessary with Melafix. Again per the package instructions you can continue to use this medication if you feel that it is needed, which leads me to believe that no harm will come of having it in the system until it is removed eventually by your normal weekly water-changes. From what I know about TeaTree oil, I'm doubtful that this medication is active anymore in the system after 24 hours have passed, anyway, so everything should be fine :) You can leave the carbon in for as long as you wish to - if you choose to use it. Carbon will stop being effective over the span of a couple of months, so I don't think you have to be terribly concerned with putting it in and taking it out again - especially with such a mild medication as Melafix is.
I hope your angel is feeling better soon! Why were his fins ragged, is he new to your tank, or is there a bully in there with him? Hope you get him back on his 'feet' and he's golden from here on out! Good luck!