Is the employee obligated to compensate the client for the cost of extracting a replacement for a lost credit card that the employee took as collateral and then forgot?

It appears that you bear the consequences of losing the card which its owner deposited with you as a guarantee for the car. This is because you are supposed to keep it in a safe place. If you did not do so, then that is a dereliction of trust (amanah), and you must pay the cost of the new card, unless its owner absolves you.