I don't know if this is an important part of the convertible headliner. I MAY protect/support the liner from the metal frame but I can't find any information on this part.

Each strip runs along the outside edge of the convertible headliner and each attaches to the front edge of the convertible frame. Both became detached from the metal frame of the convertible.

I thought I would try using Gorilla Ultra Duty Glue and use strong magnets to secure the glued edges until the glue sets and hopefully that will do the repair.