Wireless communications in the sub-THz bands are contemplated to achieve the soon required Tbit/s data rate. To fulfill this requirement, sub-THz transceivers aggregate several carriers, or in other words, implement channel bonding. In this paper we investigate the mitigation of the carrier frequency offset impact on channel bonding systems. In contrast to the literature, we consider that each of the carriers is corrupted by an independent random carrier frequency offset. Moreover, we do not address the carrier frequency offset estimation to compensate it but instead the optimization of the demodulation to mitigate the impact of this impairment. First, a system model is presented to describe channel bonding transceivers corrupted by carrier frequency offsets and the analytical expression of the resulting interference is outlined. Second, we pursue the analytical study for systems using waveforms with rectangular pulse-shaping. By evaluating the capacity, it is exhibited that a detection algorithm jointly demodulating the carriers could enhance the performance. Third, several detection algorithms are introduced and compared by means of numerical simulations. We show that a joint linear detection algorithm achieves a significant performance gain in comparison to a receiver demodulating independently the carriers.