In the file below, select the closed curves, run ExtrudeCrv, pull the extrusion downward, let go of the mouse and type T for ToBoundary, then select the solid part as the boundary. It works.
Undo, do the same thing, but instead pull the extrusion upward, let go of the mouse, type T, then select the solid - it fails, it extrudes some random distance in the opposite direction of the solid. If the input curves are moved vertically some distance away from the surface they fail to extrude at all in this second case.
I discovered this because instead of typing the first letter of the command option, I usually click on the option on the command line. Depending on the orientation of the part and whether your command line is docked on the top or bottom of the window (the direction your mouse pulls the extrusions when you go to click the option), you either get a correct result or not.
A minor related issue is the fact that the Solid menu has a direct Extrude Surface to Boundary entry, but the Extrude Planar Curve menu item does not have this as a submenu - one has to click on the command line option to activate it.
ExtrudeToBoundaryQ2.3dm (317.7 KB)