We have computed the vibrational spectrum of the helium ionized trimer He(3)(+) using three different potential energy surfaces [D. T. Chang and G. L. Gellene, J. Chem. Phys. 119, 4694 (2003); E. Scifoni et al., ibid. 125, 164304 (2006); I. Paidarova et al., Chem. Phys. 342, 64 (2007)]. Differences in the details of these potential energy surfaces induce discrepancies between bound state energies of the order of 0.01 eV. The effects of the geometric phase induced by the conical intersection between the ground electronic potential energy surface and the first excited one are studied by computing vibrational spectra with and without this phase. The six lowest vibrational bound states are negligibly affected by the geometric phase. Indeed, they correspond to wavefunctions localized in the vicinity of the linear symmetric configurations and can be assigned well defined vibrational quantum numbers. On the other hand, higher excited states are delocalized, cannot be assigned definite vibrational quantum numbers, and the geometric phase shifts their energies by approximately 0.005 eV.