δ Scuti variables are stars which exhibit periodic changes in their luminosity through radial and non-radial pulsations. Internally, these stars have relatively small convective cores, and convective overshoot can significantly affect the size. Recently, models of radial pulsation in δ Scuti stars found a strong correlation between the pulsation constant (Q) as a function of effective temperature and the amount of convective overshoot within the star. However, only models with metallicities of Z = 0.02 were examined, leaving the dependence of this relationship on chemical composition unknown. In this work, we have extended the model grid to cover a range of metallicities using MESA, and analyzed the models' pulsation properties using GYRE. By varying the models' mass, rotation speed, convective overshoot, and metallicity, we studied the behaviour of Q at low temperature. We found that the updated convective boundary treatment in MESA changes the overshoot dependence found previously, and the value of the slope depends on both rotation and overshoot. We also found that there is a metallicity dependence in the Q values. The lowest metallicity models in our grid reached higher temperatures than previously studied, revealing a parabolic relation between log Q and log T ef f .