I believe it works like this.
If the Canes were to waive him, the team that claims him with the worst record gets the claim. So if Chicago, Anaheim, or SJS put in a claim, they would get him over CLB. CLB doesn't have first right of refusal or anything like that.
If CLB claims him and is the ONLY team to put in a claim, then they can send him down without putting him on waivers again.
The Canes CAN trade him, but when the Canes originally claimed him, if another team also put in a claim (unlikely because it would have to have been a team higher in the standings than Carolina), then Carolina would have to offer him to those teams before being able to trade him.