What happens from the perspective of your counterparty (buyer-seller) when you close your option early?

Since stock options are exchange-traded (as opposed to over-the-counter, like forex options), your counter-party is actually the exchange. Ex:  You STO a call and decide to close early.  When you BTC your option, the original buyer still has the same position, but essentially the seller who sold you the call to close out your trade is now on the other side of that original transaction (with the exchange as the middleman).