We use deep, μ r ≲ 28 mag arcsec-2, r-band imaging from the Dark Energy Camera Legacy Survey to search for past, or ongoing, merger activity in a sample of 282 low-excitation radio galaxies (LERGs) at z < 0.07. Our principal aim is to assess the the role of mergers in the evolution of LERGs. Exploiting the imaging depth, we classify tidal remnants around galaxies as both minor and major morphological disturbances for our LERG sample and 1622 control galaxies matched in redshift, stellar mass, and environment. In groups and in the field, the LERG minor merger fraction is consistent with the control population. In galaxy clusters, 8.8 ± 2.9% of LERGs show evidence of recent minor mergers in contrast to 23.0 ± 2.0% of controls. This ̃4σ deficit of minor mergers in cluster LERGs suggests these events may inhibit this type of nuclear activity for galaxies within the cluster environment. We observe a >4σ excess of major mergers in the LERGs with M * ≲ 1011 M☉, with 10 ± 1.5% of these active galactic nuclei involved in such large-scale interactions compared to 3.2 ± 0.4% of control galaxies. This excess of major mergers in LERGs decreases with increasing stellar mass, vanishing by M * > 1011.3 M☉. These observations show that minor mergers do not fuel LERGs, and are consistent with typical LERGs being powered by accretion of matter from their halo. Where LERGs are associated with major mergers, these objects may evolve into more efficiently accreting active galactic nuclei as the merger progresses and more gas falls on to the central engine.