It would probably help to post a picture of the ride while it was still under construction and showing what it looks like without all the rockwork-
The gray colored steel and concrete are the structural elements. Based on the model/render, the only structural element that seems to be getting altered is that beam at the peak used to stabilize the tree trunk. That piece also isn't part of the structural integrity of the rest of the mountain.
The reddish brown "netting" seen in the photo is a thin metal mesh they use to frame and apply the cosmetic concrete over. This layer of concrete is also fairly thin. To the degree that it's relatively easy to damage. Back in 2012 when the ride was in really poor condition, there were some sections outside right before the riverboat finale that had large holes in them. The inside was hollow and you could see this metal mesh sticking out of the very thin layer of concrete. This is how the interior scenery is structured as well.
Based on the models, it looks like they're not going to be tearing much of the rockwork off of the exterior. They're keeping most of it and just applying some additional paint and vegetation to make it look more swampy. WDW's variant is even seemingly retaining the "red clay" paint. The tree trunk is probably going to take the most effort since they need to cut that one steel beam. I suspect the briar patch doesn't even have such hefty support beams since the thorns are small.