The reliable computation of shell structures requires a tool to assess and control the quality of the finite element solution. For practical purposes, the quality of the numerical solution must be measured using a quantity of engineering interest rather than in the standard energy norm. However, the assessment of the error in an output of interest is based on a standard energy norm error estimator. The standard error estimator has to be applied to both the original problem (primal) and a dual problem related with the selected engineering quantity. In shells with assumed-strain models, the combination of primal and dual error estimation is performed differently than in the continuum mechanics case. Moreover, a part from the goal-oriented error estimator, the adaptive process requires a remeshing criterion. This work introduces an specific remeshing criterion for goal-oriented adaptivity and its particularization to the context of shell elements.