This video is about Gerstner 82 Chest and Riser Theft Repair - #3. This installment deals with removal of damaged door and the removal and replacement of the strip wood.
It came out easily enough for you. But you probably could have steamed it or soaked it with a wet rag put an iron on it and gotten the original glue to release. I was able to get all of the broken parts of my grandfathers tool chest apart using similar techniques. They used hide glue originally on them. It held stronger than the wood around it for 80 years but came apart with no trouble at all with some water and heat.