High-energy narrowband terahertz (THz) pulses, relevant for a plethora of applications, can be created from the interference of two chirped-pulse drive lasers. The presence of third order dispersion, an intrinsic feature of many high-energy drive lasers, however, can significantly reduce the optical-to-THz conversion efficiency and have other undesired effects. Here, we present a detailed description of the effect of third-order dispersion (TOD) in the pump pulse on the generation of THz radiation via phase-matching of broadband highly chirped pulse trains. Although the analysis is general, we focus specifically on parameters typical to a Ti:Sapphire chirped-pulse amplification laser system for quasi-phase-matching in periodically-poled lithium niobate (PPLN) in the range of THz frequencies around 0.5 THz. Our analysis provides the tools to optimize the THz generation process for applications requiring high energy and to control it to produce desired THz waveforms in a variety of scenarios.