An intensive disturbance of the heliosphere originating from a series of solar flares at the end of May 2025 revealed itself as an extremely strong Forbush decrease in the flux of galactic cosmic rays, which was observed at the worldwide network of neutron monitoring starting from 1 June 2025. Together with an effect on the intensity of cosmic rays measured at a height of 3340 m a.s.l. by a standard NM64 neutron supermonitor of the Tien Shan High-Mountain Cosmic Ray Station, the impact of this event was detected here as a synchronous depression in the counting rates of thermal neutrons and hard gamma rays, the background intensity of which is also continuously tracked in the environment of the station. This observation may be profitable for development of an alternative technique applicable for studying large disturbances in the heliosphere, besides using the traditional method of neutron monitor. An analysis of the frequency of the events of multiple-neutron generation in the Tien Shan supermonitor demonstrated that the influence of the heliosphere disturbance on the hadronic component of cosmic rays did most distinctively reveal itself in the energy range of (3–20) GeV.