A number of scenarios have been proposed to explain the low velocity dispersion (and hence possible absence of dark matter) of the low surface brightness galaxies NGC 1052-DF2 and NGC 1052-DF4. Most of the proposed mechanisms are based on the removal of dark matter via the interaction of these galaxies with other objects. A common feature of these processes is the prediction of very faint tidal tails, which should be revealed by deep imaging (μg > 30 mag arcsec−2). Using ultra-deep images obtained with the Gemini telescopes, about 1 mag deeper than previously published data, we analyzed the possible presence of tidal tails in both galaxies. We confirm the presence of tidal tails in NGC 1052-DF4, but see no evidence for tidal effects in NGC 1052-DF2, down to surface brightnesses of μg = 30.9 mag arcsec−2. We therefore conclude that while the absence of dark matter in NGC 1052-DF4 could be attributed to the removal of dark matter by gravitational interactions, in the case of NGC 1052-DF2 this explanation seems less plausible, and therefore other possibilities such as an incorrect distance measurement or that the system may be rotating could alleviate the dark matter problem.