Put your card in a vessel and fill with acetone until the card is completely submerged. Cover the container so the acetone doesn't all evaporate, and wait 15-30 minutes.
Once the plastic has all peeled away, gently poke around in the mess to find the shiny RFID antenna and carefully remove it from the vessel. You can reuse the acetone, just pour it back into the bottle and throw the now-destroyed plastic away.
The antenna is made of enamel-coated wire, and it does not have to remain in this exact shape to still function just fine.