The PMTs of the CMS Hadron Forward calorimeter were found to generate a large size signal when their windows were traversed by energetic charged particles. This signal, which is due to Čerenkov light production at the PMT window, could interfere with the calorimeter signal and mislead the measurements. In order to find a viable solution to this problem, the response of four different types of PMTs to muons traversing their windows at different orientations is measured at the H2 beam-line at CERN. Certain kinds of PMTs with thinner windows show significantly lower response to direct muon incidence. For the four anode PMT, a simple and powerful algorithm to identify such events and recover the PMT signal using the signals of the quadrants without window hits is also presented. For the measurement of PMT responses to Čerenkov light, the Hadron Forward calorimeter signal was mimicked by two different setups in electron beams and the PMT performances were compared with each other. Superior performance of particular PMTs was observed.