Bananas are climacteric fruit: they keep ripening after harvest. Ethylene is the natural hormone that tells produce and flowers to ripen and wilt, and a ripening banana gives off ethylene of its own, which can hurry the fruit packed around it. For an exporter that means yellow fingers on arrival and less say over when the fruit is ready for the market.
1-MCP works at the receptor, not on the ethylene in the air. Moistened, the FreshTrap sachet releases a tiny dose of 1-MCP gas that occupies the plant's ethylene receptors, so the ripening signal is held back, whether the ethylene comes from the air in the carton or from the fruit itself. 1-MCP binds the ethylene receptor about 10 times more strongly than ethylene itself (Blankenship & Dole 2003).
That is also how it differs from the other products used on bananas: 1-MCP blocks the response to ethylene; absorbers (KMnO₄ sachets) remove ethylene from the air; ripening agents (ethephon) add it. How 1-MCP works explains the mechanism in full.