This article reports the influence of cosmic radiation interaction while testing the T-symmetry in metastable triplet states of positronium with the Jagiellonian-Positron Emission Tomograph (J-PET) detector. The J-PET detector developed at Jagiellonian University in Krakow, Poland is one of its kind being based on organic scintillators. J-PET is an axially symmetric and high acceptance scanner that can be used as a multi-purpose detector system. It is well suited to pursue tests of discrete symmetries in decays of positronium in addition to medical imaging. Cosmic rays have been considered as a well known source of background while performing test measurements with the J-PET detector. It is important to estimate and reject the significant contribution of the cosmic ray interactions within the J-PET detector in order to improve the sensitivity while testing T-symmetry violation. Therefore, the results of cosmic radiation uniquely being separated due to their large energy deposits in plastic scintillator detectors are shown in this article.