I remember hearing that story decades ago. However, looking at the current maps showing the difference between the geoid and the reference ellipsoid, it is hard to think about pear.
To be pear-shaped, there would have to be a deep depression at Antarctica, which does not exist, according to current measurements.
Looking only at geometry, a bulge before or around the target would cause a premature impact point only if the missile approached the target in a _very_ shallow angle. A 100 m bulge and 3 degree approach angle (e.g. airport ILS approach) would cause an impact 2 km prematurely.
In my understanding the ballistic missiles of those days approached the target nearly vertically, so the bulge would affect the impact point only a few meters, although the impact would happen perhaps 100 ms earlier than calculated.
The reason for the "bulge" is that the mass below the Earth's surface is not evenly distributed, i.e. there are low density materials (and hence less mass and less gravitation) below the bulges. The varying gravitational force along the whole flight path will cause deviations in the flight path of the missile.
This is exactly what the French Geodesic Mission did in the 18th century :-). However, you can only determine the diameter of the Earth measured on the equator and on the poles, but you can not map local variations in the gravitational field by that method.
Fortunately the two triangulation networks used by the FGM (one in Ecuador and the other in Scandinavia) happened to be on two separate "bulges", compensating for some of the errors. However, if one network had been on a bulge and the other in a depression, the error would have been larger.
Paul