If you have a 3D mesh and want a surface, then you probably want to skip the Feature Edges step.
You didn’t post your data nor even show a diagram or image, so I have to guess what your data looks like. I’m guessing the airfoil you want to see is a hole in the middle of your mesh. In that case, Extract Surface should generate this surface. But it will also generate the outer surface that envelops it, so you won’t see it. If you fly the camera inside the outer envelope, you should be able to see the airfoil in the middle. As described in the other page, you can use tools like Extract Cells By Region or Clip to remove the outer envelope.
My guess is that those spurious cells come from discontinuities in the mesh. That is, there are 2 polyhedra that are supposed to share a face, but the topology connection is not correct. Usually this is from errors in the mesh although discontinuous methods might do this on purpose.
You can try using the Clean to Grid filter (beforeExtract Surface) to merge coincident points and hopefully get shared faces to be shared topologically.
At least one of those cells must be touching the airfoil. I can’t think of any automatic way of removing those. My only thought is to remove them with an Extract Cells By Region with a carefully placed plane.