There is no facility in TexGen to export to a .obj file. You can export the geometry as a .stp or .iges file using the File->Export->STEP... or IGES... options. You can also export the surface mesh as a .vtu or .stl file using the File->Export->Surface Mesh... option. It may be possible to convert into .obj format from one of these. Bear in mind that by just exporting the geometry you lose any orientation and volume fraction information associated with the textile.