The correct lace comes threaded over a piece of heavy stiff wire. The wire is fed through holes in the cowl (4 holes on each side, two at the top near center of the car and two at the bottom)and then doubled back on itself and cut off. There is a threaded j-hook about halfway between the top and the bottom which is hooked over the hoodlace and tightened from inside the car to both center the hoodlace in the groove provided for it and to tighten it up after the wire at both ends is secure.
To remove the lace, back off on and remove the j-hook from inside the car, then cut the wire at each end with cutting pliers.
The correct replacement hoodlace with the inserted wire is available from the Filling Station (Part Number FS-285) and other suppliers. They also sell the j-hooks as Part AF-277.
Note that if your hoodlace had been replaced at some point, it is unlikely to be the type described above.
Hope that helps.
All the Best, Chip