Personally I would cut another square of black n white and put it on the glass of the window black side out to blend, cut a 10 inch hole in the sheet you have up on the wall and poke the vent thru to sit between that sheet and the window sheet. Vent wont be visible from outside and helps prevent light leaks.
When you cut the hole in the sheet, line the cut edge with duct tape to strengthen it. Will help stop the weight of the vent just tearing the black n white.
Make sure to use some kind of bug screen on the end of the vent to stop any nasties crawling in. Specially with it going directly outside. Try to angle the vent so that moisture cant run back in either
Just be careful as each bend reduces airflow.
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