The work of or connected with the restoring of the surface or pavement of the street, alley, sidewalk or public way, and back filling, shall be done by or under the supervision and control of the Department of Public Service. The above work of restoration and backfilling shall be completed in accordance with the specifications on file with the Director of Public Service. An inspector may be assigned to see that the specifications are followed. The expense of this inspection shall be part of the cost of restoring the excavation, if it be deemed necessary or expedient by the Director.