The main detector to provide data to study highly energetic (above ~400 MeV) solar particles is the network of ground-based neutron monitors (NMs). Solar events recorded on the ground are called ground-level enhancements (GLEs). All GLE-related data from the NM network are collected in the International GLE Database (IGLED, https://gle.oulu.fi), which provides formal NM count-rate increases above the constant pre-increase level which is due to galactic cosmic rays (GCR). However, the basic formal assumption that the GCR background level remains constant throughout a GLE event is often violated. We have carefully revised the IGLED and provided a new data set of de-trended NM count-rate increases that account for the variable GCR background. This had led to a significant revision of the corresponding integral omnidirectional fluences of solar particles reconstructed from the GLE data. The database of the de-trended NM count rate is revised for most GLE events since 1956. Integral omnidirectional fluences were re-assessed for 58 GLE events and parameterized for 52 reasonably strong events by applying the modified Ellison-Ramaty spectral shape. This forms a basis for more precise studies of parameters of solar energetic particle events and thus for solar and space physics.