This is how you can do it,
Pick each of your Rows and Measures in the Pivot Table and select the "Format Values" option when you click on the options menu for each of the rows and measures.
In that set the border color to "your background color" which might be "white" and then make sure the Border Position is set to "None"
that's it your pivot view will not have any grid lines anymore..
Please mark if this helps