Several users noticed the Delete button was missing when a message was selected in the Inbox:

I recently switched email accounts and the Delete button is disabled and some of my messages are missing. The Delete key on the keyboard will delete messages, only the Delete button in the Home ribbon and the right-click menu for selected e-mail(s) is disabled.

This is the result of exporting an IMAP data file to a pst file or opening IMAP pst files in Outlook. The folders retain certain IMAP features, one of which is the Delete button doesn't work as expected. (In IMAP, it purges.) To fix it, you need to edit the Inbox folder using MFCMAPI and change the PR_CONTAINER_CLASS to IPF.Note.

For a macro method, see Fix the Outlook Folder Type after Exporting an IMAP Account

1. Get MFCMAPI . If you have 64 bit office, you need 64 bit MFCMAPI.
2. Open MFCMAPI, go to Session, Logon
3. Select your profile
4. Double-click on the affected data store.
5. Expand Root - Mailbox
6. Expand Top of Information Store or IPM_Subtree
7. Select Inbox
8. Look for PR_CONTAINER_CLASS in the right pane, double-click on it.
   
9. Change IPF.IMAP to IPF.Note then click OK to close the dialog.
   
10. Repeat for each folder that was exported from an IMAP data file.
11. When you are finished, close the MFCMAPI window, click Session, Logoff on the last MFCMAPI window.

Video Tutorial

Use VBScript to change the selected folder

To use, copy and paste into Notepad then save with the .vbs extension. Select the folder you need to change then double click to run it the VBS.

PropName = "http://schemas.microsoft.com/mapi/proptag/0x3613001E"
Value = "IPF.NOTE"

Set oOutlook = CreateObject("Outlook.Application")
Set oFolder = oOutlook.ActiveExplorer.CurrentFolder
Set oPA = oFolder.PropertyAccessor

FolderType = oPA.GetProperty(PropName)

'MsgBox (FolderType)

If FolderType = "IPF.Imap" Then
   oPA.SetProperty PropName, Value
End If