Sometimes players end up with Card Pieces they have no interest in collecting.
So far, we do not have a system in place for selling or deleting unwanted Card Pieces.
If you only have Card Pieces for cards that you don't want to collect, you can leave an "open deck" for you opponents. This means setting up a very weak deck and making sure that anyone who attacks you successfully takes a Card Piece from you. This can effectively reset your Card Pieces over night.
Specific Card Pieces might not be very common, and not many players in your ratings area may have those pieces. In this case, playing a quest that can reward you with that kind of card piece is the best way to go.