Rocket is right. Unfortunately, roughing up may be a problem going forward. You want 3m 051131 06382 half-inch Automotive Plus Acrylic Attachment Tape. Use a 1-1/2" drywall knife (joint compound spreader) to carefully scrape the adhesives off both the door and the trim. You can use Prep-Sol, Pre-Cleano, or any other brand of adhesive remover (body shop wax and goo remover for pre paint prep) to clean both surfaces, but I highly suggest for the backside of the trim, use regular old Lacquer thinner (carefully keeping it on the backside only). It is actually much better if this surface is as smooth as possible. Lacquer thinner will begin to soften the rubber compounds in the trim and after it flashes (evaporates enough to look dry), the 3m tape will literally instantly bond to the trim - you will NOT get a chance to reposition it. Just like the factory trim adhesive tape, use two strips per trim piece, one along the top backing and a parallel one along the bottom. Once you have the tape on the trim piece, strip the first 6 inches of cover tape away and (hopefully you already noted the exact positioning) start attaching the strip on the panel. Have a helper keep stripping away tape about a foot ahead of your contact location and keep going, using the body groove line as your guide keeping gaps even. I use a roller (old wallpaper seam roller about an inch wide) to roll up and down the trim after it is on.
When I worked in the body shop, we used masking tape every 6" to hold it in place for a few hours, but that was so 70's, this stuff doesn't require it.
Keep that lacquer thinner FAR away from your paint though! It will immediately soften your dissolve your finish.
Hope this helps,
Ron