I doubt soaking will help. In some of the cases I have found that the card falls off the tape with paper loss even without trying to remove it yourself. You can see in the Flick below that is settled into the bottom right corner already before extraction.
My theory is that these were designed to work without tape, but once they started building them they realized they banged around and were off-center, maybe they ordered the wrong size. Rather than redesign, they decided to call it a sunk cost, bought some double-sided tape, and moved on.
I often tell people who are trying to sell these to break apart or remove that the break-up value may be substantially less than they think. Assume paper loss in any purchase for these reasons.
I learned this the hard way a couple of years ago…
Fortunately, I was harvesting the Wilbur Good signature, and found a better place for it in my custom “Signature Collection” jumbo.
