Pull points from mesh edge to curve

Hello,

Not used to work with mesh and mesh tools, I’m trying to select the points from the mesh edge and pull them to a near curve I drawn.
I joined a very simple 3dm for example, the file I’m working with is far more complex.
I would avoid snapping manually all the points from mesh edge to the curve.
Thanks for help
Pull mesh points to crv.3dm (40.5 KB)

The solution for this example will probably not apply to the real one.

I would verify the “probability”