I converted the surface mesh I had into a tetrahedral form using TetWild. The script provided a surface mesh output for the new form as well. I performed UV mapping on this output using Blender and added as child object and used as physics and collision geometry as in the tutorial. At this point, my object became a deformable one with texture mapping as in the screenshot below.
Has been resolved, needs to deal with the UV partition in the SurfaceMeshCut.
Only Example-PBDThinTissueCut has been processed so far. Pending further testing