The video above gives a step by step process of carefully removing the insert from an Odyssey putter without completely destroying it. This method also works on some Ping putters and possibly other brands. Read on to see examples of what is found once the insert is removed.
Above is an image of an Odyssey original White Hot #4 putter with the insert removed. The assembly process for this insert probably involved:
a. pouring an epoxy into the pocket
b. placing the white insert at a designated depth
c. then wiping across the putter face to form a smooth border
This was a quick 3-step process at the factory where the insert was locked into place around it's perimeter, and back face, once the epoxy hardened. The epoxy also conveniently made a nice black border, when viewing the front face.
The downside is over time, this epoxy may harden to become brittle and eventually the insert could fall out. As can be seen above, the epoxy did crack in places when it was removed. This was not helped with the heat from the boiling water, but still, the aging is evident.
Removing the insert from an Odyssey White Hot Tour #1 was a bit different to the aforementioned original White Hot. The insert is held in with a double-sided tape, which can be seen at the base of the pocket in the image above. Besides the Tour series, this was also used in the XG, and White Ice. This is most likely a great product by 3M called VHB tape.
Odyssey still use this process today, as well as other manufacturers like Ping. The advantage is speed of assembly. The disadvantage would be accuracy. Tape is rarely a precise thickness material, therefore it is difficult to ensure insert flatness if used for installation. The double sided tape also has a soft stiffness, which could provide an added forgiveness when the insert makes contact with the ball. This is often characterized as "spongy" by players.
Removing a putter's insert is not for everyone. However, with a bit of work, the putter can be optimized into something more functional, aesthetic, and personal, e.g. the Odyssey Rossie XG picture above. Once the insert is removed, it is key to remove all reminants of previous tape or epoxy. Your new insert must bond to a clean surface free of particles or contaminants. This provides a long bond life, as well as accurate insert height. The USGA insert height tolerance is +0.006"/-0.004"