For any system communications (emails or banner messages) with deliverability set to Upon Approval, they will be sent to the User Messages queue.

Distributing messages from the User Messages queue:

1) Go to Site > Communications > User Messages

 User-added image

2) Filter the User Messages Queue by desired column(s)
User-added image

3) Mark the Select/Deselect All Checkbox
User-added image

4) Select Distribute from the Act on Selected Menu
User-added image

5) Select green Distribute button
Distribute Messages Dialog Box
Note: If you have more than 50 messages selected, be sure to mark the box to "Also distribute # messages from other pages" Distribute Messages Module

Deleting messages from the User Messages queue:

To delete messages from the User Messages queue, follow the same steps as above, and select Delete in Step 4.  A pop up window will appear allowing you to confirm the decision.  To confirm, click the green Delete button. 
Warning: Once messages have been deleted, the action cannot be undone.
Confirm Delete button