It has been well established that the orbital magnetization of interacting electrons can be simply evaluated by applying the single-particle formula to self-consistent Hartree-Fock (HF) bands. However, we show that such a procedure fails qualitatively for orbital magnetic susceptibility, especially in topological systems: in a Chern-insulating phase of twisted MoTe2, the interaction-induced correction reverses the sign of the susceptibility. This result follows from an algebraic framework that solves the HF problem at finite magnetic field, where noncommuting canonical momenta obstruct a direct calculation: a reverse Peierls substitution maps every magnetic-translation-invariant operator to a unique bivariate function, converting the finite-field self-consistency into a function equation that can be expanded systematically in B. At first order, this yields a linear equation for the field-induced change δX of the Fock potential, leading to an intrinsically interaction-induced susceptibility in addition to a single-particle-like one. The framework reproduces the Středa formula for insulators, and an auxiliary-Hilbert-space construction carries it to periodic and moiré systems. Finite-field HF calculations in a gapped Dirac model and in the twisted MoTe2 Chern insulator confirm the theory quantitatively.