May be these lines came from one corner-point (to see superposed points) on your strokes.
So 2 solutions: To reconstruct (Ctrl R) your stroke, and to verify to have only curve-points; or you can add curve point on the stroke, then delete the corner point.

In your file .3dm, there is no strokes of construction, so we cannot delete these lines. Generally to don't meet this kind of problem, we keep all the lines of construction. A trick: you select all the lines of one objet (or more), you give a name like "myobjet_fils (strings, lines, or what you want), then you hide these lines. The lines are useful if you want to change the curves on your objet for any reason, or if you want rebuilt it, without lost time.

Good MoI

PS. That make me think to a function that you will be good to find in MoI: The possibility to convert a corner-point to a curve-point, and vice-versa.
And another one that misses terribly in MoI: to make one group with associated objets.