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 NGC1052-DF2 and NGC1052-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 (μ(g) > 30 mag/arcsec2). 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 NGC1052-DF4, but see no evidence for tidal effects in NGC1052-DF2, down to surface brightnesses of μ(g)=30.9 mag/arcsec2. We therefore conclude that while the absence of dark matter in NGC1052-DF4 could be attributed to the removal of dark matter by gravitational interactions, in the case of NGC1052-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.