When your zeolite is already ammonia exchanged and calcined it is not the "iron" in form as charge compensation Fe-cations you want to get rid of, but the ironoxide.
Iron tends to form oligomeric species or even FeOx-clusters and Fe2O3 Particles in zeolites. After thoroughly ion echange and calcination most of the remaining iron will be Fe2O3 in my opinion.
I am not sure if you can really remove these particles without changing the zeolites composition by leaching processes or destroying the structure because of the perhaps quite big ironoxides particles.
A very mild leaching with HCl (no more than 0.1 N) is known to work. The conditions depend on the (varying) Fe level in your natural zeolite sample. A quick check in the litterature should give you conditions; however you will have to adjust them to the properties of your specific natural zeolite. Verify that no dealumination takes place by chemical analysis (a side reaction taking place under harsh conditions of T, time, concentration of acid...) and check crystallinity and pore volume. Keep also in mind that natural zeolites are made of large crystals and diffusion issues (evacuation of the Fe debris from the micropores) might cause problems such as inhomogeneous removal of Fe (and Al) across the crystals.