We investigate the impact of ionizing external ultraviolet (UV) radiation on low-mass haloes (
) at high redshift using
baryonic resolution zoom-in simulations of seven regions from the THESAN-ZOOM project. We compare three simulation sets that differ in the treatment of external UV radiation: one employing a uniform UV background initiated at z=10.6 in addition to radiation transport for local sources, another with the same background starting at z=5.5, and the default configuration in which the large-scale radiation field from the parent THESAN-1 simulation box acts as a boundary condition. The multi-phase interstellar medium (ISM) model, combined with its high mass resolution, allows us to resolve all star-forming haloes and capture the back-reaction of ionizing radiation on galaxy properties during the epoch of reionization. When present, external UV radiation efficiently unbinds gas in haloes with masses below
and suppresses subsequent star formation. As a result, in simulations with early reionization, minihaloes fail to form stars from pristine gas, leading to reduced metal enrichment of gas later accreted by more massive haloes. Consequently, haloes with masses below
at all simulated epochs (z>3) exhibit lower metallicities and altered metallicity distributions. The more accurate and realistic shielding from external UV radiation, achieved through self-consistent radiative transfer, permits the existence of a cold but low-density gas phase down to z=3. These findings highlight the importance of capturing a patchy reionization history in high-resolution simulations targeting high-redshift galaxy formation. We conclude that at minimum, a semi-numerical model that incorporates spatially inhomogeneous reionization and a non-uniform metallicity floor is necessary to accurately emulate metal enrichment in minihaloes.