The study explores the dynamic response behavior of distributed feedback terahertz quantum cascade lasers under varying self-injection intensities of the optical field, utilizing the Lang-Kobayashi equation alongside a newly introduced modified end face reflection coefficient. This coefficient describes the coupling effect of distributed feedback gratings on the intracavity optical field. With increasing intensity of the self-injected light field, the laser transits from a steady state to a periodic, quasiperiodic, or chaotic state. Notably, compared to the conventional semiconductor lasers, terahertz quantum cascade lasers exhibit stability under larger self-injected intensities. Upon manipulating the target reflector, the output signal from a distributed feedback terahertz quantum cascade laser, operating in steady, periodic, and quasiperiodic states, can accurately describe the movement law of the reflector. However, in a chaotic state, the laser's output signal appears distorted. Comparing with the typical steady-state solution models reveal that the proposed theoretical model furnishes more accurate output signal patterns. This study provides theoretical support for articulating the dynamic behavior of quantum cascade lasers with grating structures, and explores the potential of distributed feedback terahertz quantum cascade lasers in the application of self-injection imaging technology.