In some cases the obstruction is 2-torsion, such as in Koschorke's example, which is an immersed surface (formed from 3 Möbius bands, with a triple point) that does not lift to a knotted surface, but it has a double cover that does lift.
The passage describes a specific type of obstruction that arises from the geometry of immersed surfaces, specifically those formed by three Möbius bands with a triple point. The obstruction is characterized by its two-torsion nature, which means it has a particular topological property related to knots and their relationship to surfaces.