In the rare-earth pyrochlore Tb₂Ti₂O₇, there are strong interactions between crystal field and phonon excitations resulting in the hybridization of crystal field excitations with both acoustic and optical phonon excitations, which may be implicated in its evasion of the expected long-range ordered states. The magnetoelastic coupling mechanisms are thought to involve large quadrupolar matrix elements between the crystal field states that allow them to couple with intersecting phonons. The character of the hybridized modes can be determined by polarized neutron scattering, as is done here for the case of a crystal field-optical phonon coupling. The coupling mechanism can be further investigated by applying a magnetic field to modify the energies of the crystal field states relative to the phonon spectrum. For a weakly dispersive optical phonon and crystal field level, this has the effect of detuning the quasidegeneracy necessary for hybridization and suppressing the magnetoelastic signal. For a strongly dispersive acoustic phonon crossing a crystal field level, the magnetic field moves the crystal field level, changing the wave vector and energy at which the modes intersect. The field-driven modification of matrix elements for dipole and quadrupole operators involved in the formation of the coupled mode results in the suppression of the magnetoelastic coupling. As the crystal field states shift to higher energy and the magnetoelastic coupling is suppressed, the spin system is driven closer to classically anticipated ordered structures.