From your description, it sounds like it’s the offside plastic panel that covers the main underbody that’s damaged. The good news is that it should be easy to replace as it’s just held on with screws. The not so good news is that’s unlikely to be the cause of your damp problem. I’m pretty certain those plastic panels are there primarily to protect against corrosion, preventing road debris / road salt from being constantly blasted at the underbody when the car’s being driven, but I don’t think they seal the underbody against water ingress. Any seams in the car body shell would have had a seam sealer applied in the factory prior to painting the body shell, and it’s this seam sealer, together with the various rubber seals around the door and tailgate openings, rear light clusters etc. that prevent the ingress of water into the car. If the plastic underbody panels are removed, the car should still be watertight.
Is it just the carpet in the rear right hand side footwell that’s damp? Have you checked under the rear seat base and in the spare wheel well under the boot floor for damp? Does the roof lining at the rear of the car above the boot area show any signs of water staining or dampness? I’d check to make sure the rubber seals around the rear offside passenger door and around the tailgate aperture are not damaged, and that they’re firmly in place. Also check that the seals around the rear light clusters aren’t damaged, and that the two rubber concertina sleeves for the tailgate wiring above the tailgate opening are firmly in place and not damaged. Two causes of water ingress on the mk7 Golf is poor sealing around the tailgate hinges above the tailgate opening and faulty seals between the speakers and the doors, so worth checking those too.
