As of this morning, I can’t delete "A Visit from Slowcake’s Amanuensis", and even though I took an action on the card it won’t go away. Similarly, I can’t delete "An Unsigned Message". They don’t have "Cannot Delete" buttons under them; instead, they have no buttons at all.
If you happen to like using that addon but want to delete an opportunity card, there are some alternatives that don’t involve deleting+reinstalling/editing the mod; which might be helpful for anyone reading this who is in a similar situation as Jonquil. :-)
Switch to another web browser temporarily.
If you have a laptop (or any other PC really), using its browser is an option.
Most of the time I just grab my mobile/cell phone, use its browser to discard the unwanted opportunity card (on the rare occasion it’s necessary to do so), and carry on.