My previous TT has that type material: Black, flexible, woven looking (?), and had a lot of saggy places. I don't know how many times I would be inspecting everything under the TT and find another tear that I have no idea of how it got there. IMO: The only option is to keep taping the tears or rip all of that stuff off. But then who knows what's behind there. My newer TT has the "Coroplast" type stuff which appears to me to be a type of plastic corrugated material. I will say this Coroplast material seems to stay put better and doesn't tear. Worse yet a friend of mine has an underbelly material that is aluminum and somewhat like corrugated roofing material. This stuff has locking hems on each side and is a bear to remove and put back into place.
2015 FR Freedom Express 310BHDS pushing a 2014 GMC Sierra CC