I notice it has a thick black line around it, which if I am honest, I don’t really understand what this means… I tried the trick of drawing lines through it, and this helped in some areas, but not others:
When you get to the stage where you show the selected face in your screen shots, select everything, right click and choose Intersect Faces>With Selection. You should then be able to remove the face skinning the hole.
Alternatively, you can trace one edge of the hole with the Line tool. Then select and delete the skinning face.
Drawing lines through it can help in some cases but it creates more stuff to erase than simply tracing and existing edge.