When you go to remove the old one, again, I would use a wide putty knife and slide it up between the windlace and the headliner so as to release the old windlace from the teeth (albeit the teeth are grabbing the headliner first and the windlace secondarily), moving it along as you slide the knife up and down as you carefully pull the windlace down.

The new windlace has an excess fabric edge which, although long enough to be grabbed by the teeth when in place, may not be long enough for you to grab it's edge, create a fold for the putty knife, and still still be long enough for the teeth to grab while you are installing. This is why I suggest sewing an additional piece of fabric onto that edge. Tape might work, but it might work against you, getting stuck on the body or the headliner. Again, if the fabric edge is wide enough, this may not be an issue. Make sense?