Can't delete vertices in Maya
I've tried Delete, Backspace, Ctrl+Delete, Ctrl+Backspace, Shift+RMB -> Delete Vertex, Mesh -> Delete Vertex. Even deleted history of this mesh. And it's still not deleting.
You need to switch to face selection mode, select and delete the face.
You need at least 3 points to support a surface. Deleting the third point will confuse maya.