The chrome trim pieces on the A-posts and the chrome along the rain gutter are expensive pieces that you want to get off the car in good shape if at all possible.  They are held in place by a sticky black substance – sort of like tar.  In addition, the chrome on the A-posts has set screws on the door side of the post that you remove. Working on a hot day and having a blow drier to further heat the glue is not a bad idea here.  Take your time and be careful. Very gentle nudging and jiggling will get them free eventually.  The worse thing you can do is rush this and then bend the pieces.

Heating up the glue on the A-post chrome finishers in order to remove them without bending them. The screws have already been removed.

The chrome finisher from the A-post strip being removed.

Once the A-post finisher is removed you can then start to work along the chrome rain gutter strips and get them off the car.  Take it slow and gentle and they should come away. There are some gobs of glue – so a blow drier can help.

Removing the chrome rain gutter strip from a Jaguar E-type