After an item is claimed and the emails have been sent, it is up to the offerer and claimant to contact each other and complete the transaction by transfering the item.
A claim on an Individual Title will remove it from the list of offerings so that no one else may claim it. A claim on a Multiple Item offer does not automatically remove it from the list of offers. A claimant may wish to claim only some portion of the offer. If this happens, it is up to the offering institution to update the Comment on the item to indicate which portions are no longer available. If the entire Multiple Item offer is claimed, the offering institution should open the item and click the All Claimed button. Clicking All Claimed will remove the item from the list of offers but leave it in their institution's history.
Delete Item should only be used to remove an item entered in error.
If a claiming institution contacts you to cancel a claim they have made, open the item and remove that institution's claim from the list. For an Individual Title, the item will be restored to the list of offers. For a Multiple Item offer, there is no other action. The item will remain in its current state.
See: Parts of the Screen | My Submitted Items for more information on opening and editing an existing item.