  We compute the one-loop contributions to spin-averaged generalized parton
distributions (GPDs) in the proton from pseudoscalar mesons with intermediate
octet and decuplet baryon states at nonzero skewness. Our framework is based on
nonlocal covariant chiral effective theory, with ultraviolet divergences
regularized by introducing a relativistic regulator derived consistently from
the nonlocal Lagrangian. Using the splitting functions calculated from the
nonlocal Lagrangian, we find the nonzero skewness GPDs from meson loops by
convoluting with the phenomenological pion GPD and the generalized distribution
amplitude, and verify that these satisfy the correct polynomiality properties.
We also compute the lowest two moments of GPDs to quantify the meson loop
effects on the Dirac, Pauli and gravitational form factors of the proton.
