If this item is given to Sturges or Proctor Ingram, then taken back via pickpocket or some other means, it will remain in the player's inventory as a quest item provided the player chooses a course of action other than the Nuclear Option.
It is possible to give both Sturges and Proctor Ingram the holotape. After giving the tape to one of them, they create their own personal copy. To complete the other questline, they will give the original back through a dialogue option.
pc When using an Xbox controller on a PC, the on-screen instructions ask to press X to insert the holotape. The correct instructions are to press A to insert the holotape and X to remove it. [verified]