We do map paths even on private property... so good call not deleting it outright. I would take these steps to resolve the fixme tag you've added.

1. Add new nodes on either end of the trail where the fence and barbed wire are. Add them as "Barrier" nodes.
2. Add a tag to the new section of path in the middle: "access": "private".
3. Remove the fixme tags.

Thanks for contributing to the map!