If you have an insert removal tool you can heat the tool, not the carbon but you need to be very specific with the heat as heat will damage carbon. Heating the tool should heat the insert (aluminum) and allow you to pull the insert out. You will need to be pulling as it is being heated so it pulls immediately when ready and excess heat isn't applied to the carbon. Keep the flame away from the end of the arrow as carbon/glue used to keep carbon wrap together will ignite.

Inspect and reinspect as noted above.