Control Points to a Curve

Hello Forum friends, probably this is an easy one or not, how can I attach control points from surfaces to a curve, is it possible to do it all at once or the long way one by one…? Please see the image, the control points to the magenta curve. Thank you!

but what would you gain from that? only moving the control points to the curve will not allign the surface. then rather use flow or rebuild it.

Why do you want to put the control points on the surface? As encephalon said the curve will not be on the surface.

The Pull and Project commands can be used to put a curve on a surface.