I suppose if you wanted to avoid disassembly, you could very, very carefully use Super Glue to attach something to the damaged badge that might allow you to pull it out — in my experience, the adhesive was essentially double-sided tape, and I would expect it to give way.
You might also use a drill with a small bit to pierce the badge and pull it out. You run the risk of damaging the plastic beneath the badge, but that will ultimately be hidden.