How can I send my client an Invoice without an item?

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 real-time. So if they've got the link ope,n they'll automatically see the change without needing a fresh email.