Continuous measurements of ground-based neutron monitors (NMs) form the main data source to study high-energy/high-intensity solar energetic particle (SEP) events, called ground-level enhancements (GLEs). All available data are collected in the International GLE Database (IGLED, http://gle.oulu.fi), which provides formal NM count-rate increases above the constant pre-increase level due to galactic cosmic rays (GCR). This dataset is used to reconstruct energy spectra of GLE events. However, the assumption of the constant GCR background level throughout GLE events is often invalid. Here we made a major revision of the IGLED dataset and provided a dataset of detrended NM count-rate increases accounting for the variable GCR background. The formal GLE count-rate increases were corrected for the variable GCR background which may vary significantly during GLE events. The corresponding integral omnidirectional fluences of SEPs were reconstructed for all GLEs with the sufficient strength from the detrended data using the "effective rigidity" method. The database of detrended NM count-rate has been reset for all GLE events since 1956. The integral omnidirectional fluences have been estimated for all the GLE evens and parameterized for sufficiently strong ones by the modified Ellison-Ramaty spectral shape. The IGLED has been revisited to account for the variable GCR background. Integral omnidirectional fluences reconstructed for most of GLE events, have benn added to IGLED. This forms a basis for more precise studies of parameters of SEP events and, thus, for Solar and space physics.