Yes, I too had been fighting this issue and the solution for me as previously mentioned was to set my Remote Desktop Connection settings under the Display settings tab to full screen. This is configured in the RDC connection log on window, which by default will only show the fields for your user ID, password and domain - you have to click on the Options button to fully display all of the various settings options, tabs, etc. that you may want to pre-configure before you connect to the remote computer. Setting the display to full screen rather than some lower resolution setting removed all of the grid lines!! Any setting less than full screen produces grid lines for me.
http://www.microsoft.com/en-us/download/confirmation.aspx?id=22465 if you have Windows XP x64 – Mark Jeronimus – 2015-07-22T10:01:48.437