How can I join vinyl decking to metal door frame?
Based on questions answered in chat you have a case where the contractor didn't measure the deck properly, and built it too high, could not flash properly under the door frame, and performed a "some genius" move putting a transition strip (meant for interior use) over top of the door frame and the vinyl, with caulk under neath.

Stupid.

Two options:  1 cheap and temporary, 1 expensive and proper.

Cheap: Use proper caulk (props to @tester101) 



Option 2 - and the door is old so this isn't actually a terrible idea.

Replace the door.  In the process, raise the rough opening of the door frame half an inch or so - however much is necessary to be able to put a proper piece of flashing under the door frame and over the vinyl.

You will probably have to custom order a door to fit your new rough opening, but at least you can seal the door area properly.

And props to @bmitch for pointing out that flashing needs to run the entire width of the deck.