Replacing Drvrs Door jamb rubber trim?

I would not remove that black screw unless you know for sure what it is holding in place. It likely has nothing whatsoever to do with the door trim. As for replacing the rubber gasket, you have to remove the old gasket entirely, and clean the channel. The new gasket should be glued into the channel (you will see how the old one was installed, usually with a black trim glue). You do not want to install the new gasket over remains of the old one as it won't fit in properly.

When I've done rubber gaskets on various cars, I've always used 3M Weatherstrip Adhesive. It is obnoxious stuff to work with, but it is very effective. You have to put it on the gasket, and also put it on or in the channel where the gasket is going to be installed, let it set up for a couple of minutes, and then install the gasket. But you have to work very carefully, because the stuff sticks immediately, so no repositioning if you make a mistake. Done right, it will last for 20 years or more. I would not use any of those silicone adhesives as they tend to peal over time, the 3M stuff is specifically designed for installing rubber trim pieces.

p.s. Look at how the old trim was installed. Some rubber gaskets fit into channels, other stuff (most of what I've seen) get's glued in place.

 

Any source for the rubber piece with the blue tape.on it?