Refining a [Character] or [GF] class card will destroy the original card in your inventory. In general it is not considered worth it to do this you can eventually refine items and cards upwards in to the items gained by doing a refined level [Character] or [GF] card though it will take a lot more time to do this.

As Karifean said, you can actually retrieve a [Character] or [GF] card refined on disc 4 however it is not so simple as they make it sound.

To begin, you must have completed both the Queen of Cards and the Garden Card Club side quests in full. This will be time consuming and also very difficult especially if you do not eradicate the card rules (excluding Same-Wall and Open plus a trade rule of your choice, these can stay since Same-Wall requires Same to be activate in the region to be actually used) in the world which you will likely need a FAQ on how to do and where to find the easiest/earliest possible changes you can make to a regions rules (such as changing Trabia Rules in Deling City ect)

Secondly you must find the Ragnorak on Disc 4 after Time Compression takes place when you find it you can use it to find the Queen of Cards in the compressed world.

Thirdly, Challenge her she will agree to play so long as she can randomly select the rules for the game. I believe she chooses a regions ruleset to use hence you need to eradicate the original rules in each region and spread only the beneficial open rule. I may be wrong and she actually uses completely random rules to play you but basically she will have access to any unique cards you refined throughout your game. I know some people have deliberately refined all but their "hand cards" and played for them back to give them a boost in the final battle this in my humble opinion is an overrated tactic since Ultimecia's castle is not hard by any means of the definition. The Queen of Cards will no longer be playing using "easy going" rules like she does in the quest when you give her cards to generate new ones she'll play decisively harder and with [Character] or high power [GF] cards in play will be a force to be reckoned with using the ALL rule is highly disadvised.