Beyond spectral quantities, Symanzik Effective Theory (SymEFT) predictions of the asymptotic lattice-spacing dependence require the inclusion of an additional minimal basis of higher-dimensional operators for each local field involved in the matrix element of interest. Adding the proper bases for fermion bilinears of mass-dimension 3 allows to generalise previous predictions to matrix elements of those bilinears. These results can be incorporated in ansätze used in continuum extrapolations and should allow improved control of the associated systematic uncertainties. Potential difficulties and pitfalls are being highlighted. The current work is limited to the use of Wilson or Ginsparg-Wilson quarks in both sea and valence.