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Option Explicit
Sub Test()
    Dim pMxDoc As IMxDocument
    Set pMxDoc = ThisDocument
    
    Dim pGCS As IGraphicsContainerSelect
    Set pGCS = pMxDoc.PageLayout
    
    
    Dim pTElement As ITextElement
    Set pTElement = pGCS.SelectedElement(0)
    
    Dim pFTS As IFormattedTextSymbol
    Set pFTS = pTElement.Symbol
    If Not pFTS.Background Is Nothing Then
        If TypeOf pFTS.Background Is ICallout Then
            MoveAnchor pFTS.Background, 0, -0.5
            pTElement.Symbol = pFTS
            pMxDoc.ActiveView.Refresh
        End If
    End If
End Sub

Public Sub MoveAnchor(pCallout As ICallout, dx As Double, dy As Double)
    Dim pPoint As IPoint
    Set pPoint = pCallout.AnchorPoint
    pPoint.X = pPoint.X + dx
    pPoint.Y = pPoint.Y + dy
    pCallout.AnchorPoint = pPoint
End Sub