You have two options to remove an invoice from the invoices screen: archive or archive and delete.
When you archive an invoice it is still viewable by clicking the Archived filter.
If you want to permanently delete the invoice, click the red Delete button under the Archived view.
Once an invoice is deleted, it is gone for good. So make sure you really want to delete it.
Remember, you can download a PDF of your invoice for your records, just in case, before deleting it.