I have this curve but I don't need this edge marked with an X, I can't select the edge and delete it.
Workaround I found is to convert it back to mesh then delete the edge, then convert back to curve. Is that the proper workflow?
In Edit mode, select the two control points defining the Edge, then use Y to split them, then X to Delete.
You can also select the 2 vertices and press X (Delete) > Segments