I would fill the existing holes with epoxy and let it setup and then reattach using existing holes in trim. Some of the dollar stores here in Canada have small syringe type epoxy dispenser with a mixing nozzle built into the syringe.I have used them to do just what you need to do. It is easy you just squeeze the syringe with the nozzle in the screw hole and go to the next one when the hole is full. Then scrape off the excess before it hardens.
Cost is $1.25 per syringe, so not very expensive and real handy.
I usually use the expensive stuff for a small job and it is no good a month later for the next project. These work great for small projects.
Second idea would be to get a box of toothpicks and glue them into the holes using epoxy or Gorilla glue.
