If you just want to send them an Invoice without this item what you can do is
1 - Edit the Signed Contract
2 - Then remove the item in question
3 - Manually mark the project as signed (Article)
4 - Click 'Send to Client'
Now your client will receive an Invoice without that item.
The link your client received will also update in realtime. So if they've got the link open they'll automatically see the change without needing a fresh email.