I will admit first and foremost that this is not an area of expertise so if anyone has any secrets or tips of the trade please bring them on!
The bungs in the teak of our interior are all extremely difficult to get out. Not only have they expanded a bit so they want to bring the wood around them out with them but they were also glued in! It makes for some very cautious work and even then I was not always successful in keeping everything pristine.
But here is a step by step process that I found to work the best (sorry about the dust all over the wood we were doing some grinding earlier):
#1: Once you’ve located the bung, take a screw of the appropriate size and slowly screw it in. If the bung doesn’t come loose and pull out, CAREFULLY keep going and the threads will rip out the surrounding wood.
#2: I used a marlin spike, which is usually handy, to gouge out the rest of the wood. I especially tried to get all the debris out of the head of the buried screw.
#3: Find the appropriate screw driver or bit and very slowly unscrew the fastener. This was surprisingly the hardest part. The screws were corroded in place and I had to turn the drill to an impact setting to break them free.
While we are at it, I came across these very small, very fragile teak trim pieces. I successfully removed them with even more care using a painters multi-tool to work them out a few millimeters. I then removed the finishing nails with a small pair of needle nose pliers.