I've had to repair that area myself.
Gorilla tape is hit and miss - it doesn't stick very well to that kind of material. Even after wiping the area down with solvent and applying the tape it would seem to be fine and then fall off later. I ended up using a piece of plastic cardboard from a sign shop and screwing it into a wood floor joist I found.
The company my DW works for actually does this kind of work on the bottom of mobile homes. The professionals that patch the material (called rodent barrier) use spray on contact adhesive and another piece of the material to create a band-aid of sorts. It holds up well.