My screen door arm bracket started pulling off of the door jamb. Unfortunately, it was a few days before I noticed, so I've already lost one corner of the bracket (I plan to replace the bracket, because it's also a bit bent up). More unfortunately, it pulled out because the area behind the bracket is pretty chewed up, something which only came to light after this happened.
I know that there are putties that are used to fill a gap in wood, but I'm also given to understand that they're generally not great to try to screw things into since they have no particular anchor to the wood around them. Is there a better solution, maybe filling in the area, then nailing a piece of wood over it to provide a more solid anchor?