Cell-free massive multiple-input-multiple-output (CF-mMIMO) is a next-generation wireless access technology that offers superior coverage and spectral efficiency compared to conventional MIMO. With many future applications in unlicensed spectrum bands, networks will likely experience and may even be limited by out-of-system (OoS) interference. The OoS interference differs from the in-system interference from other serving users in that for OoS interference, the associated pilot signals are unknown or non-existent, which makes estimation of the OoS interferer channel difficult. In this paper, we propose a novel sequential algorithm for the suppression of OoS interference for uplink CF-mMIMO with a stripe (daisy-chain) topology. The proposed method has comparable performance to that of a fully centralized interference rejection combining algorithm but has substantially less fronthaul load requirements.