Drip rail caulk?

There's something like caulk or putty in the drip rail of my 65 Dart wagon. It has shrunk and curled, there are pieces missing, and it seems like it's mainly a place to trap moisture now.

What is this stuff? How can I get it out, just by scraping? What should I put in there to replace it, something other than just paint?

thanks in advance -