Experimental and theoretical studies on runaway electrons (REs) in tokamaks are a major focus of current fusion research [1], particularly for high-plasma-current devices like ITER and next-generation fusion reactors. Among various detection methods, bremsstrahlung emission (both thin and thick targets) in the hard X-ray (HXR) energy range is widely used to diagnose REs. Unlike conventional HXR monitors (HXRM) in present tokamaks, the ITER-HXRM is specifically designed to withstand extreme load conditions expected during plasma operations while providing measurement in a wide range [2-6]. The ITER-HXRM employs an optical fiber bundle and lens assembly to couple light output from the scintillator to the PMT. This configuration introduces significant light attenuation that modifies the statistical nature of the detected signal and impacts energy resolution. Recently, for the first time, the full prototype of the ITER-HXRM system has been successfully tested in a tokamak environment during the experimental campaign in the ADITYA-U tokamak [7]. The test results are in agreement with the conventional HXR spectrometer configuration (i.e., Scintillator-crystal directly coupled with the PMT) and validate the present design considerations. Experimental observations demonstrate that energy-resolved HXR spectra can be obtained in the counting-mode operational regime up to ~1 MHz count rate. As a next step, characterization of the Runaway Electron (RE) Energy Distribution Function (REDF) is essential for understanding their dynamics in tokamak plasmas. The measured HXR-spectra convoluted with the emission of bremsstrahlung photons from REs reaching the detector and the detector response function. Thus, the deconvolution of HXR-spectra into REDF is necessary. In this work, we present reconstruction studies of the runaway electron energy distribution function by applying the deconvolution technique to the measured HXR spectra registered by the prototype ITER HXRM in ADITYA-U tokamak discharges. The de-convolution technique employs detector response functions and bremsstrahlung emission transport matrix from source to the detector, calculated using Montecarlo codes, and viewing geometry. These results establish the capability of an ITER-HXR diagnostic to provide information on runaway electrons under realistic tokamak conditions, along with identifying key limitations imposed by detector physics and high-flux operation. This work contributes to the validation of ITER diagnostic and forward modelling frameworks required for reliable runaway electron characterization in future fusion devices. References: [1]. B. N. Breizman, et.al., Nucl. Fusion 59,083001 (2019). [2]. Santosh P. Pandya, et.al., Phys. Scr. 93 115601, (2018). [3]. Santosh P. Pandya, PhD thesis, Aix-Marseille University, (2019), https://theses.fr/2019AIXM0036 [4]. S. Kajita, et.al., Plasma Fusion Res. 16, 1302106, (2021). [5]. Patryk Nowak vel Nowakowski, et.al., Rev. Sci. Instrum. 93 103512, (2022). [6]. Ansh Patel, et.al., Phys. Scr. 98(8), 085604, (2023). [7]. Patryk Nowak vel Nowakowski, et.al., Rev. Sci. Instrum. 97, 033509, (2026).