i don't know if i got your question, but the linestrip shoudn't connect the last vertex to the first one. first, make sure you are drawing everything in the correct order you need. if you put a vertex in top left corner and the next one in bottom right, you'll have a line crossing this space, no matter what's inside. maybe the code could help undertanding what you want to do and what's the problem.
anyway, if you want quads without a fill color, you can use sf::Quads and set the FillCollor to sf::Color::Transparent.