We experimentally demonstrate more than four-orders of magnitude enhancement in third harmonic generation from an amorphous silicon layer as thin as 10 nm deposited above silicon nitride guided mode resonance (GMR) structures under a conical mounting condition using a rectangular aperture as a pupil plane mask for the fundamental excitation. The multilayer GMR structure studied here consists of shallow etched one-dimensional silicon dioxide gratings with a silicon nitride intermediate layer and an amorphous silicon nonlinear medium. Under conical mounting, by restricting the fundamental excitation angles along the grating vector direction, while retaining the angles supported by the objective lens along the grating lines, the resonances are made angle insensitive. The forward detected THG enhancement increases from 2860 in the absence of any pupil plane mask, with a uniform fundamental excitation angular span of 2.3° to 4740 and 1.7 × 104 in the presence of rectangular apertures that selectively reduce the excitation angular span along the grating vector direction to 0.86° and 0.43°, respectively. Conical mounting using rectangular aperture pupil masks to engineer the fundamental excitation is a promising approach to enhance nonlinear optical processes from angle sensitive GMR structures.