Abstract <p>The hypothesis that supernova remnants are key sources of Galactic cosmic rays gains support from evidence that HESS J1731-347 one of the few Galactic objects capable of accelerating hadronic cosmic rays to TeV energies may harbor an exotic strange quark star rather than a conventional neutron star. This conclusion stems from its unusually low mass and compact radius, which challenge standard neutron star models. If confirmed, such a quark star could generate cosmic rays through the transition from the two-flavor color-superconducting (2SC) phase to the color-flavor-locked (CFL) phase, potentially releasing strangelets, hypothetical strange quark matter (SQM) particles. Detecting these strangelets in cosmic rays would provide groundbreaking evidence for quark matter. The future Cherenkov Telescope Array (CTA), with its unmatched sensitivity and spectral resolution in the very-high-energy (VHE) gamma-ray regime, is uniquely positioned to search for their annihilation or decay signatures. We analyze theoretical predictions for these gamma-ray signals and evaluate CTA’s potential to detect or constrain them. Additionally, we present an in-depth assessment of CTA observations of HESS J1731-347, focusing on spectral features that could confirm strangelet production. A positive detection would not only validate the existence of strange quark stars but also establish a direct link between quark matter and cosmic-ray acceleration, reshaping our understanding of compact objects and high-energy astrophysics.</p>