Do butterflies pass over migration patterns to their offspring?
If you think about it, monarchs must have a pretty strong genetic component to migration since often they only make one round trip at most in a lifetime. But its not as simple as passing a map in the DNA.  

If a mountain springs up on the route, the 'common sense' of the butterflies are still operational and they will tend to find their way around it.  

The paper discussed here is older.  More recent Monarch butterfly migration  of some genetics that have been done shows some traits that are related to migration patterns by sampling over many butterflies whose patterns vary tremendously.  

Glancing over the paper, I'd say that there may be some 'muscle' memory in migration, but probably the mechanisms encoding the route of migration are not yet discernable.  This is far from something we understand well. 

The insect is following patterns of behavior but doesn't turn into a robot just because its migrating.  Migration patterns are probably linked to a series of environmental cues.  

Changes in climate or shifts in magnetic fields can change migration patterns. Butterflies would be very different than say migratory birds in terms of the social and environmental markers for migration.