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 different 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.
If the holotape is activated from within the Pip-Boy it will still say "Internal Network Detected" and then stay there until the Pip-Boy button is pressed again to exit the tape.
pcxboxone If using a Xbox controller on a PC the on screen instructions to press X to insert the holotape are wrong. The correct instruction should be press A to insert the holotape and X to remove it. Rules minded people can appear to be stuck in the Institute if trying to follow the instructions.