If you know which footnote you want to delete, highlight its index (number
shown in superscript in the document) and press Delete.

Programatically, try:

Sub aa()
For Each fnote In ActiveDocument.Footnotes
If 0 = Len(Replace(fnote.Range.Text, " ", "")) Then
fnote.Range.Delete
End If
Next
End Sub

This will delete footnotes that are empty (len=0) or just spaces (visually
empty).