At the Fair each summer for that past few years I have done a little demo on this topic. Mike is right, its best not to make the inletting mistakes in the first place. But, sometimes the guacamole hits the fan and there it is - the dreaded gap.
There are two options make the metal bigger or make the wood bigger.
Lots of times, some strategic peening of the back of a metal part can push the metal over so that the metal part fills the gap. I have taken a hammer to a barrel tang on occasion, peening the edge, so the metal flowed over and widened that tang. In the case here in this string that would not have been a good option unless the barrel flat could be widened too. But, sometimes a little hammering on the barrel flat widens the top flat of the barrel enough that the tang can be widened to fill a gap.
The other alternative is to make the wood bigger. In this thread, the wedges of wood shown above is one way of making the wood bigger, but I have some concerns about how it was done. It appears that the wood wedges were made with the wood grain running up-and-down. This will put end-grain wood along the tang. End-grain wood always takes stain very aggressively and generally results in a very dark piece of wood on the finished gun. If I have to make a wood filler, I always try to make the filler piece with the grain running the same way as the wood it will be glued to. I adjust the chip-breaker on my plane well away from the edge so I get ribbons of wood rather than chips. Then I adjust the depth of the blade for a cut as deep as the gap I need to fill. I take a plain maple board, tilt the plane to produce a ribbon with a wedge cross-section and make a filler ribbon. This ribbon can be moistened, coated with glue on the side that will be in contact with the stock wood and then installed to fill the gap, tapping the filler wedge down into the stock between the metal part and the inlet with a little wooden dowel to get a compressed-tight fit. Once dry the excess can be trimmed off. Done well, the resulting glue line is on the order of a thousandth of an inch thick, virtually invisible, and the wood grain is the same in the filler as in the stock adjacent. Staining makes the repair invisible. That's how I would have approached the task that is the subject of this thread.
Best Regards,
John Cholin