Elimination among orders:
Zoraptera and Mecoptera are considered separate, more derived insect lineages and are not generally described as the bridging group between Orthopteroid and Hemipteroid insects, so both are ruled out.
Psocoptera (booklice) is closely related to lice but is itself grouped within the Hemipteroid assemblage rather than serving as the connecting order.
That leaves Phthiraptera (lice), whose mixture of chewing/sucking mouthpart types and simplified wingless body plan is why it is treated as the transitional order linking the two insect groups.