You need to remove the border to get the lines from the template to go
away.  Since it's a template form, open up InfoPath, select Design a
Form->Customize a Sample Form->Select "Resume"

Right click on the object (textbox, etc.) and choose "Borders and
Shading" and select "None" to remove the border.  You'll need to do
this for every view that you want to see without borders.