How to fix this storm door hinge?
Go to your home store and pick up a package of dowel pins or just get one big dowel rod and a drill bit to match.They come in many sizes depending on the hole you're trying to repair.

Drill out the eroded wood, squirt some wood glue in the hole and tap in the dowel pin and let the glue dry.

If you are going to use one long rod and cut it to the size you need, cut a small grove length wise in your pin to allow excess glue to escape. This isn't needed if you buy a package of dowel pins because they are already grooved. After the glue dries, sand and paint the area and then you can reinstall the jab bracket.