I am pretty sure the graphic is showing super position of field lines. That is the field lines of E due to q are shown. The decreasing magnitude is due to the E field decreasing over distance like $1/r^2$.

Your last sentence tells me you think it is a conductor. If you know that the sheet is a conductor as opposed to a dielectric, the above must be true. We know this because as you say the charge on either side of the plane will shield the other side from the point charge.