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CaFe₂O₄ is a quantum antiferromagnet that exhibits an interplay between two different magnetic phases below T_Neel ~ 200 K. We have analyzed the terahertz (THz) response of CaFe₂O₄ for the polarization configuration h_ω||c and e_ω||b and observed a significant change in the spectrum between 80 K and 120 K for frequencies above 900 GHz. The THz dielectric permittivity shows hysteresis between 80 K and 120 K that does not occur for any other orientations. In addition, we have observed a magnon with a frequency of 840 GHz at 10 K that red shifts with increasing temperature until 70 K. At which point, its spectral weight decreases rapidly, while at the same time a lower frequency magnon gains intensity. This behavior is only observed for h_ω||c irrespective of the direction of the electric field of the THz pulse. These behaviors seem to be associated with the decrease in the population of the B magnetic phase and simultaneous increase in the population of the A phase around 100 K.