I'm guessing that you know not to remove any vertices from the MS skeleton - but just reallocate them? I went through a painful learning curve when I created some uniforms a while back
Fortunately in this case the vertices of the talkie are part of a fully separate mesh from the puppet's uniform/body, not sharing any of them, so just had to proceed selecting carefully those vertices and faces of the gadget to be removed. Well, a few times I peeked the wrong vertex/face and an ugly hole appeared on the puppet's body; good old undo command came handy to repair the damage done to the victim.
In other cases, messing with the mesh most probably would require moving some of the vertices or deleting them and recreating some of the zapped faces, but the latter can be quite involved and quickly become a real hell of a mess.
Nevertheless, in the example shown, in addition to editing the mesh of the model, I had just to doctor a bit the textures in order to remove what appeared to be the shadow of the talkie projected over the uniform.