The Galerkin modal expansion is a well-known method used to develop reduced order models for thermoacoustics. A known issue is the appearance of Gibbs-type oscillations on velocity fluctuations at the interface between subdomains and at boundary conditions. Recent work of Laurent et al. (2019) and Laurent et al. (2021) have shown that it is possible to overcome this issue by using an over-completed frame, instead of a Galerkin modal basis. However, the low-order modeling based on this frame modal expansion may generate spurious modes. In this paper, the origin of these non-physical modes is identified and a method is proposed to automatically remove them from the outcome. By preventing any interaction between the physical and non-physical components, the proposed methodology drastically improves the robustness and reliability of the frame modal expansion modeling for thermoacoustics.