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Context. Galactic cosmic rays (GCRs) and solar particles with energies greater than tens of MeV penetrate spacecraft and instruments hosted aboard space missions. The Solar Orbiter Metis coronagraph is aimed at observing the solar corona in both visible (VL) and ultraviolet (UV) light. Particle tracks are observed in the Metis images of the corona. An algorithm has been implemented in the Metis processing electronics to detect the VL image pixels crossed by cosmic rays. This algorithm was initially enabled for the VL instrument only, since the process of separating the particle tracks in the UV images has proven to be very challenging. Aims. We study the impact of the overall bulk of particles of galactic and solar origin on the Metis coronagraph images. We discuss the effects of the increasing solar activity after the Solar Orbiter mission launch on the secondary particle production in the spacecraft. Methods. We compared Monte Carlo simulations of GCRs crossing or interacting in the Metis VL CMOS sensor to observations gathered in 2020 and 2022. We also evaluated the impact of solar energetic particle events of different intensities on the Metis images. Results. The study of the role of abundant and rare cosmic rays in firing pixels in the Metis VL images of the corona allows us to estimate the efficiency of the algorithm applied for cosmic-ray track removal from the images and to demonstrate that the instrument performance had remained unchanged during the first two years of the Solar Orbiter operations. The outcome of this work can be used to estimate the Solar Orbiter instrument's deep charging and the order of magnitude for energetic particles crossing the images of Metis and other instruments such as STIX and EUI., Comment: 8 pages, 6 figures