In this Letter we investigate the origin of the Oosterhoff dichotomy in light of recent discoveries related to several ancient merging events of external galaxies with the Milky Way (MW). In particular, we aim to clarify if the subdivision in terms of the Oosterhoff type between Galactic globular clusters (GGCs) and field RR Lyrae (RRLs) can be traced back to one or more ancient galaxies that merged with the MW in its past. We first explored the association of GGCs with the past merging events according to different literature studies. Subsequently, we compiled the positions, proper motions, and radial velocities of 10138 field RRL variables from Gaia Data Release 3. To infer the distances, we adopted the MG-[Fe/H] relation, with [Fe/H] values estimated via empirical relationships involving individual periods and Fourier parameters. We then calculated the orbits and the integrals of motion using the Python library Galpy for the whole sample. By comparing the location of the field RRLs in the energy-angular momentum diagram with that of the GGCs, we determined their likely origin. Finally, using Gaia G-band light curves, we determined the Oosterhoff types of our RRL stars based on their location in the Bailey diagram. The analysis of the Bailey diagrams for Galactic RRL stars and GGCs associated with an "in situ" versus "accreted" halo origin shows remarkable differences. The in situ sample shows a wide range of metallicities with a continuous distribution and no sign of the Oosterhoff dichotomy. Conversely, the accreted RRLs clearly show the Oosterhoff dichotomy and a significantly smaller dispersion in metallicity. Our results suggest that the Oosterhoff dichotomy was imported into the MW by the merging events that shaped the Galaxy.