There’s the TNG episode where Federation scientists are observing a non-warp capable civ from on the planet, when an accident exposed their lab and the aliens take one of the scientists hostage thinking they are demons. In this case, the external influence they are trying to limit and fix is the federation itself.
There is also another in the same vein where Data is damaged during an away mission on a planet with a non-warp capable civ and inadvertently is spreading radioactive material around the settlement because he lost his memories, and then has to correct all the damage when he is repaired.
These are the only two I can think of that even come close while also being within Federation space. As others have pointed out, the Voyager episode where they run into the Farenghi that ended up there from another episode of TNG is the exact thing you are asking… Just not in the right part of space.
There’s the TNG episode where Federation scientists are observing a non-warp capable civ from on the planet, when an accident exposed their lab and the aliens take one of the scientists hostage thinking they are demons. In this case, the external influence they are trying to limit and fix is the federation itself.
There is also another in the same vein where Data is damaged during an away mission on a planet with a non-warp capable civ and inadvertently is spreading radioactive material around the settlement because he lost his memories, and then has to correct all the damage when he is repaired.
These are the only two I can think of that even come close while also being within Federation space. As others have pointed out, the Voyager episode where they run into the Farenghi that ended up there from another episode of TNG is the exact thing you are asking… Just not in the right part of space.