To edit a Snapped Bézier curve:
The key points on the curve are displayed:



The curve forms the new shape and remains on the surface of the model.

You can use a keyboard shortcut to offset points on a Snapped Bézier curve where the points have dependencies on a surface.
To offset points on a Snapped Bézier curve:
or Ctrl and
to offset the curve points. If the curve points have dependencies to a surface, they are offset along the surface normal on the curve.