This study is primarily focused on the behavior of propagation of waves through a homogeneous and isotropic thermoelastic half-space using the modified Green-Lindsay theory of thermoelasticity, along with the effects of non-local and two temperature (TT) parameters. A new set of governing equations is formulated and solved using the reflection technique after reducing the equations to two dimensions and a dimensionless form. The impact of different parameters namely non-local parameter, TT parameter, and impedance parameters along with different theories of thermoelasticity are shown graphically on amplitude ratios obtained from reflected waves i.e., longitudinal wave (LD-wave), thermal wave (T-wave), and transverse wave (SV-wave). The modified Green-Lindsay theory is widely used in fields such as heat transfer, and geophysics with potential practical applications in areas such as earthquake engineering and materials engineering. The study also includes the deduction of particular cases based on the obtained results.