When you open a Distribution List do not get confused with the Delete vs. Remove functions.

Notice the Delete function is part of the Actions Group for the distribution list.
If you select Delete, the distribution list is gone.

The Remove function is part of the Members Group.
Click to Open the distribution list
Go to Distribution List tab
Highlight the name that is to be removed
Click the Remove icon and click the Update Now icon.
Then Click Save & Close to save the changes.

If you accidentally deleted the Distribution List / Contact do not panic.
Go the Deleted Items folder


Search for the Deleted Contact
Drag the contact over the Contacts folder
The folder should be returned to its proper place in the Contacts Folder.