| Actually, it's not that hard to get the strip out of the back of the neck. Heat is the way you do it. Silicon blankets are very helpful here, halogen lights much less so. Once the strip is out of the groove it can be scraped clean of the glue. The same techniques are employed on the walls of the rout. White or yellow glue is applied with a brush and the strip is clamped back into place. A small strip of wax paper can be fitted to the back of the truss rod first to prevent any squeeze out from coming into contact with the truss rod. Finish touch up follows.
Injecting glue into the joint is risky. There is no way to keep the glue from interfering with the rod's ability to perform it's function. Most woodworking glue's strength would be seriously compromised by the dilution necessary to get them to wick into the joint. Liquid thin CA glue is the exception. However, there are two problems with using it. The first is the same as above, there is no way to control where it will penetrate, how far, and what kind of damage it will cause when it gets there. The second is a matter of strength. CA glues have very little sheer strength. And that is exactly the job we are asking it to do when gluing the strip back in. A healthy amount of force applied to the truss rod will pop the filler strip right back out. Now you've got an even bigger mess.
CA glue would be the number one choice for touching up the finish, though. | 
