From Wiki:
...protected by state law in Arizona.......
Conservation status
Gila monsters are listed as near threatened by the IUCN.[1] They are listed as “Apparently Secure” by NatureServe.[44]
In 1952, the Gila monster became the first venomous animal to be given legal protection.[45] They are now protected in all states of their distribution. International trade in the species is regulated under Appendix II of CITES.
Looks like a good target for a .410 shotgun, much of Arizona is open country, who is to know?