This study examines a supply chain including a live-streaming platform and a manufacturer who sells its products via the platform in the agency or resale mode. Under the carbon trading system, the manufacturer adopts green technology and makes greenwashing behavior, and the platform chooses whether to use blockchain to eliminate this behavior. The adoption of green technology generates a higher (lower) production quantity at a low (high) initial unit product emission. Considering blockchain’s impact on the optimal operational decision, the existence of greenwashing generates a higher profit for the platform in the agency mode. In the resale mode, the existence of greenwashing generates a higher (lower) profit for the platform if the additional profit brought by blockchain is low (high) at a low or moderate cap. However, when the cap is high, the existence of greenwashing hurts the platform’s profit. By considering the government’s decision, it is discovered that (a) the existence of greenwashing hurts (improves) the social welfare at a high (low) correlation coefficient between the carbon trading price and potential market demand, and (b) the agency mode always generates higher social welfare than the resale mode.