BiTeI is a giant Rashba spin splitting system, in which a noncentrosymmetric topological phase has recently been suggested to appear under high pressure. We investigated the optical properties of this compound, reflectivity and transmission, under pressures up to 15 GPa. The gap feature in the optical conductivity vanishes above p~9 GPa and does not reappear up to at least 15 GPa. The plasma edge, associated with intrinsically doped charge carriers, is smeared out through a phase transition at 9 GPa. Using high-pressure Raman spectroscopy, we follow the vibrational modes of BiTeI, providing additional clear evidence that the transition at 9 GPa involves a change of crystal structure. This change of crystal structure possibly inhibits the high-pressure topological phase from occurring.