Simple test:
Can you export as pdf and see if you have the same problem? I don't know if pdfs fit into your workflow though.
Not so simple solution:
Duplicate the green boxes onto a new layer and set the fill to none. (Make sure this new layer is above the green boxes layer.) Then make the layer with the green boxes non-printing by double clicking on the layer name and deselecting the check box "Print Layer"
Depending on how many spreads and templates that you have this could take a bit of time. Sorry.
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