Is the fuel burn for a satellite launch affected by the position of the moon relative to the launch site? The gross mass of a satellite rocket is tiny compared to that of Earth, and Luna. Between them, however, the two bodies set up tides in bodies of water which itself is again considerable mass. 
At the point of launch a satellite rocket might not be affected by the Moon's gravitation attraction. As it goes higher/ more distant from earth/closer to escape/ target orbit do it's fuel burn statistics change depending upon the position of the moon vis-a-vis launch location/payload release location?
 A: No, there is no change to the fuel burn statistics due to the Moon. An intuitive answer to this would be that if there were some change, such as a decrease in fuel consumption when the moon is overhead, then NASA/ESA/etc would always be waiting for the moon to be overhead before launching. Since they don't do this, it is safe to say there is no difference.
A more scientific answer would be that the Moon does not have enough influence over a satellite to affect it in any significant way.
Let us perform an analysis. Satellites normally don't go any closer to the Moon than geosynchronous orbit - about $42000~km$ in radius. Let's take a $17000~kg$ satellite nearing this altitude and say that the Moon is directly overhead. Then, on average the satellite would be $342000~km$ from the center of gravity of the Moon, which would mean it experiences a net force due to the Moon of around $6N$. This means an acceleration of $3.5*10^{-4} m/s^2$ towards the Moon. Again, this means that in the course of an hour, the Moon could add a maximum of around $1.3 m/s$ to the satellite's velocity. Given that a satellite at that orbit has a velocity around $3km/s$ and that lower satellites have faster speeds, it is safe to say that the Moon does not contribute in any significant way to changing the velocity during the launch/orbital insertion phases and as such, does not change the fuel statistics of launching a satellite.
