As described in https://link.springer.com/content/pdf/10.1007/s00158-019-02281-z.pdf (Section 3 Example 2) and Berggrens paper, a function maps the back to the original value at the unperturbed mesh, and thus does not have a material derivative.
If you want to implement this, you can create your own custom expression in dolfin, and add the adjoint and tangent linear actions, see http://www.dolfin-adjoint.org/en/release/documentation/time-dependent-wave/time-dependent-wave.html.