Set the pivot table to preserve formatting:
On the pivot toolbar, choose PivotTable>Table Options
Add a check mark to 'Preserve formatting', click OK
Remove the check mark from AutoFormat Table
Click OK
You may have to enable selection (From the Pivot toolbar, choose
PivotTable>Select, and click on Enable Selection)
On the PivotTable toolbar, choose PivotTable>Select>Entire table
On the Formatting toolbar, click the arrow at the right of
the borders button
Click the No Borders button (at the top left)
If the you find that the borders return after you refresh the pivot table,
you could record a macro as you refresh and reformat the pivot table.
Then, run that when you want to update.