This is one of the more important exercises in the chapter. The problem asks for a proof that it's possible to absorb a coordinate transformation directly into the Lagrangian. If you can do this, you can express your paths and your forces in whatever coordinates you like, so long as you can transition between them.
I also found that this exposed, and repaired, my weakness with the functional notation that Sussman and Wisdom have used in the book.
The problem states:
Show by direct calculation that the Lagrange equations for $L'$ are satisfied if the Lagrange equations for $L$ are satisfied.