To delete a gift, login to your account and hover over the item you would like removed to click trashcan icon located at the top right portion of the gift(s).
If you are deleting an item you imported from a store registry, you will need to login to that store registry and delete the item there. You can immediately re-sync the registry by clicking Sync Store Registries from the top of your member homepage. Hover over the logo of the store you would like updated and click Re-Sync. Otherwise, your MyRegistry gift list will automatically update the changes within the next 24 hours.