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Non-Hermitian systems have attracted considerable attention for their broad impacts on various physical platforms and peculiar applications. In non-Hermitian systems, both eigenvalues and eigenstates simultaneously coalesce at exceptional points (EPs). As one of the remarkable features of EPs, the field chirality is commonly considered perfect, which is utilized as an intriguing feature to control wave propagation and regarded as a criterion of EP. However, in this work, we discover an imperfect chirality of eigenmodes at the EPs in an optical whispering gallery mode (WGM) microcavity perturbed by two strong nanoscatterers. This counterintuitive phenomenon originates from a strong frequency-dependence of the scattering between the counterpropagating waves at an "effective scatterer", which could be explained by a first-principle-based model considering a dynamic multiple-scattering process of the azimuthally propagating modes. We find that the generally imperfect chirality at the EP tends to be globally perfect with the decrease of the scattering effect induced by the nanoscatterers. Furthermore, the chirality also becomes locally perfect with the decrease of the relative azimuthal angle between the two strong nanoscatterers. This work provides a new understanding of the general properties of chirality at EPs. It will benefit the potential applications enabled by the chirality features of non-Hermitian systems at EPs.