Laser-induced growth of optical damage can limit component lifetime and, therefore, increase operating costs of large-aperture fusion-class laser systems. While far-infrared (IR) lasers have been used previously to treat laser damage on fused silica optics and render it benign, little is known about the effectiveness of less-absorbing mid-IR lasers for this purpose. In this study, we quantitatively compare the effectiveness and efficiency of mid-IR ( $4.6\mathrm{\mu m}$ ) versus far-IR ( $10.6\mathrm{\mu m}$ ) lasers in mitigating damage growth on fused silica surfaces. The nonlinear volumetric heating due to mid-IR laser absorption is analyzed by solving the heat equation numerically, taking into account the temperature-dependent absorption coefficient $\alpha (T)$ at $\lambda =4.6\mathrm{\mu m}$ , while far-IR laser heating is well described by a linear analytic approximation to the laser-driven temperature rise. In both cases, the predicted results agree well with surface temperature measurements based on IR radiometry, as well as subsurface fictive temperature measurements based on confocal Raman microscopy. Damage mitigation efficiency is assessed using a figure of merit (FOM) relating the crack healing depth to laser power required, under minimally ablative conditions. Based on our FOM, we show that, for cracks up to at least $500\mathrm{\mu m}$ in depth, mitigation with a $4.6\mathrm{\mu m}$ mid-IR laser is more efficient than mitigation with a $10.6\mathrm{\mu m}$ far-IR laser. This conclusion is corroborated by direct application of each laser system to the mitigation of pulsed laser-induced damage possessing fractures up to $225\mathrm{\mu m}$ in depth.