If you want to process tables from the cursor position, then set a range to the area you wish to process e.g.
Code:
Sub Macro2()
Dim oRng As Range
Dim oTable As Table
Dim oBorder As Border
Set oRng = ActiveDocument.Range
oRng.Start = Selection.Start
For Each oTable In oRng.Tables
For Each oBorder In oTable.Borders
oBorder.LineStyle = wdLineStyleNone
Next oBorder
Next oTable
End Sub