Abstract In view of their advantages for memory and storage applications, the quest to find suitable magnetic thin film heterostructures that can exhibit strong spin pumping effect persists in the scientific community. Here, the spin pumping phenomenon is investigated in Galfenol (FeGa) thin films by systematically varying the thickness of heavy metallic Ta underlayer (UL). The films exhibit soft magnetic properties with a bcc‐phase and a notably low Gilbert damping is obtained for FeGa on Si (100). The precessional magnetization dynamics of Ta/FeGa films are explored using the time‐resolved magneto‐optical Kerr effect technique, revealing the presence of a resonant Kittel mode and additional strain‐induced modes. The lowest value of effective Gilbert damping in Ta/FeGa is obtained as ∼0.015, which rises by ∼65% as the thickness of UL increases. Spin pumping and two‐magnon scattering mechanisms are validated using a ballistic spin transport model. An overall effective spin mixing conductance value of ∼5.48 × 10 15 cm −2 is found, which is the highest value ever reported in magnetostrictive Galfenol films. Additionally, micromagnetic simulations are explored to understand the effect of tilted magnetic anisotropy on the formation of magnetic modes in these films. These findings in FeGa films establish it as an effective spin source material and offer innovative ideas to control spin‐wave propagation and diverse applications in straintronics.