I had a person in mind who lived out of town to become a pet sitter. I wanted to just send a message to her, however, the message went to the world. I would like to delete the message on facebook but do not have the standard que in the corner.
Typically anything you post on Facebook can be edited or deleted by you. Just go to the message and click on the tiny arrow (more like a "v") just above the message on the right side. Click it and there should be options to edit and delete. If that arrow isn't there, then definitely contact Facebook support.
Sounds like this would be a question for Facebook's support team. If you aren't able to delete the message from the drop down menu in the upper right corner, perhaps it will let you change the privacy settings for that post? One of the options you can select is that only you can see it. It won't delete it, but at least it won't be visible to everyone.