Despite the high degree of frustration introduced by half-garnet sublattice of magnetic ions, and its single ion ground state being the non-Kramers (quasi-)doublet, terbium gallium garnet(Tb3Ga5O12, TGG) orders magnetically at TN~260 mK. Additionally, it displays wide range of magnetoelastic phenomena, e.g. thermal Hall effect, which is currently under our investigation, as its origins are not known yet. This effect was also observed in TbTi2O7, where it seems to be suppressed by field-induced long-range-order. Due to the high resemblance between those two materials, we are convinced that full understanding of thermal Hall effect in TGG requires knowledge of its mechanism of ordering, which has been previously assigned to hyperfine interaction. In our preceding study we have observed significant softening of the low-lying exciton band at ordering wave-vector, while approaching TN. This cannot be explained by hyperfine interaction. We propose a detailed experimental investigation of temperature dependence the exciton gap. It would shed a new light at the dynamics of induced-moment systems and provide us the data necessary for revealing the roots of thermal Hall effect.