It's an applique. It's either glued on or pin nailed. Just pop it off, clean the surface and apply new bead molding.
If glued on, you might want to delicately cut the glue line on the outside edges, with a razor or sharp box knife, so that the underlying wood (veneer?) doesn't split, when you lift/pop it off. For those older pieces, the glue might be hide glue, which, in that case, you might can heat it with a blow drier (not real hot) and the glue will soften, allowing for ease of lifting.
But see if you can determine if it is pin nailed, rather than glued. For an old item, I suspect it may be glued, though.