Found a thread talking about stuffing Foam Backer Rod
inside the existing weather stripping
I am going to take a look at the "hole" to see what (if any) size backer rod will fit.
: Checked the gap in the weather stripping and it is pretty large so I think I am going to go get some 1/4", feed it through, and see if the door still closes. I will let you know how well it works.