Hi,
There seems to be a little misunderstanding here. If you have a travelcard then it is valid to use National Rail as well as the Underground within the zones covered. Charlton is in zone 3 so you’d need a zone 1-3 travelcard.
Alternatively, if you are using PAYG then the whole journey will be charged as one from Charlton to your zone 2 destination as long as you don’t take longer than 20 minutes between touching out at London Bridge NR and touching back in at London Bridge LU.