This is how it worked when the unslotting was automated. I assume (possibly incorrectly), that the same would hold true now.
When you unslot, EVERYTHING gets removed from the weapon. Anything you pay to keep you can slot back in the weapon (assuming you also paid to keep the weapon).
You pay for what you KEEP, not for what gets destroyed.
In your example of a TTH Suiken, in order to keep all 3 cards and the weapon, you would need to pay $13. You could then put the two TT cards back in the Suiken, and do whatever you wanted with the H card.
If you only paid for the Suiken and the H card ($9), the two TG cards would be destroyed.