Dealing with homophones when playing "Contact" (Conversation Game)
Since they're pronounced the same, there's no way of knowing that the guesser and defender are referring to different words. The reasonable thing to do in that case is accept the correct guess and move on appropriately (a loss for the defender, in this case, if I'm reading the rules correctly). 

In this particular case, the guesser may have spoken the word so as to emphasize the difference in spelling (drawing out the 'o' sound in capitol). In that case, it seems very reasonable for the defender to respond with "not capitol" (again, drawing out the 'o' sound at the end). This will likely point to "capital" as being the next guess (especially with the addition of the 'a' from the defender).

Unless, that is, somebody asks which spelling of the word you are referring to (maybe red vs read). The standard rules linked don't say anything about homophones, so it's probably best to decide beforehand what happens in that case. Given that this seems to be a kind of party game, accepting the homophone as a correct guess seems the most appropriate, as it creates less conflict and more fun, and keeps the game moving.