Cannot Remove Borders or Gridlines in Microsoft Word
First, let's not confuse borders with gridlines. The rule of thumb is that borders print, and gridlines do not. This is true in Word and Excel, and probably many other Windows applications.
Gridlines, which are viewable and do not print (unless specifically set to print), can be viewed by choosing, from the menu, Table Show Gridlines. When you are already viewing gridlines, then the same menu option changes and Show Gridlines is not available, but Hide Gridlines is.
Gridlines appear gray. If your gridlines appear to print, then they're likely gray-colored borders.
Some borders and gridlines information:
You cannot remove gridlines. You can only choose to view them or not.
You cannot turn gridlines off for other users. Viewing of gridlines is a machine setting, it is not a document setting. When you send your document to others, you cannot control whether they see your table gridlines or not.
You can turn off all borders in a table by clicking inside the table and hitting Ctrl+Alt+U, or click inside the table and (from the menu) choose Table Select Table, then Format Borders and Shading, click on the Borders tab and choose None.