Many geophysical and geochemical phenomena in the Earth's interior are related to physical and chemical processes in the outer core and the core-mantle boundary, directly linked to isotopic composition. Determining the composition using standard geophysical methods has been a challenge. The oscillations of atmospheric neutrinos, influenced by their weak interactions with terrestrial matter, offer a new way to gather valuable information about the Earth's internal structure and, in particular, to constrain the core composition. If neutrinos had as yet unknown non-standard interactions (NSI), this could affect their propagation in matter and consequently impact studies of Earth's composition using neutrino oscillation tomography. This study focuses on scalar-mediated NSI and their potential impact on atmospheric neutrino oscillations, which could obscure information about the hydrogen content in the outer core. In turn, compositional uncertainties could affect the characterization of NSI parameters. The analysis is based on a Monte-Carlo simulation of the energy distribution and azimuthal angles of neutrino-generated $\mu$ events. Using a model of the Earth consisting of 55 concentric shells with constant densities determined from the PREM, we evaluate the effect on the number of events due to changes in the outer core composition (Z/A)$_{oc}$ and the NSI strength parameter $\epsilon$. To examine the detection capability to observe such variations, we consider regions in the plane of (Z/A)$_{oc}$ and $\epsilon$ where the statistical significance of the discrepancies between the modified Earth model and the reference model is less than $1\sigma$.