The security policy changed from the traditional “castle and moat” approach to the zero-trust security model due to the recent change in work styles. The authors have been developing the overlay network protocol, called CYber PHysical Overlay Network over Internet Communication (CYPHONIC), to support the zero-trust security model easily. Additionally, we have designed an essential function of a gateway device called a CYPHONIC adapter because the proposed protocol requires devices to install a special client program. The initial implementation suffers from performance degradation of Transmission Control Protocol (TCP) due to order changes of packets during packet handling functions. This paper redesigns the adapter functions focused on the packet processing scheme of the CYPHONIC adapter and confirms the throughput improvement in standard protocols.