Okay, it appears it is the option "Smart Cut and Paste that causes the issue with not being able to delete the space directly:
Code:
Sub ScratchMacro()
'A basic Word macro coded by Greg Maxey
Dim oRng As Range
Dim bSCP As Boolean
bSCP = Options.PasteSmartCutPaste
Options.PasteSmartCutPaste = False
Set oRng = ActiveDocument.StoryRanges(wdFootnotesStory)
With oRng.Find
.Text = " ^p"
While .Execute
oRng.Characters.First.Delete
oRng.Collapse wdCollapseEnd
Wend
End With
Options.PasteSmartCutPaste = bSCP
lbl_Exit:
Exit Sub
End Sub