The possible existence of two dark-matter-free galaxies (NGC 1052-DF2 and NGC 1052-DF4) in the field of the early-type galaxy NGC 1052 presents a challenge to theories of dwarf galaxy formation according to the current cosmological paradigm. We carried out a search for signatures of past interactions connected to the putative hosts of NGC 1052-DF2 and NGC 1052-DF4 using a very deep L-band image obtained with the 0.7 m Jeanne Rich telescope that reach a surface brightness limit of 28.5 mag arcsec(-2) in the r band. We found several low-surface brightness features, possibly consistent with an ongoing merger history in this group. We find a tidal interaction between NGC 1052 and NGC 1047, confirming a physical association. Furthermore, we find a stellar loop around NGC 1052 in the direction of NGC 1042 and a stellar stream pointing in the direction of NGC 1052-DF2, but they are not directly connected. We find no evidence for a recent tidal interaction for NGC 1052-DF2 and NGC 1052-DF4. No LSB features have been uncovered around the spiral galaxy NGC 1042, which leaves the association (physical or projected) between NGC 1052 and NGC 1042 ambiguous, although they have similar radial velocities. Their association will only be established when accurate distances to both objects have been measured.