It can possibly be removed and reglued. But it would certainly require some minor patchwork to fill in the hole that gets drilled into it to remove it. It may be the better option to remove it and replace it completely with a new plug. Grain matched to the butt (if you can even see the grain), finish it, checker it and color match.
The plugs are for weight holes. Either to add weight or, more commonly, remove weight.
Even if a hole was under a buttplate/pad, the factory would still put in a wooden plug. As an aside, this is also the same way that I do it if I need to drill out a weight hole. Just last week I was balancing two guns that I am restocking. One needed 1oz removed and the other needed 1.5oz removed in order to balance and match lettered weights. I drilled 1” holes and they got thin wood plugs afterwards. Under the buttplates.
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B. Dudley
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