Siemens IS the owner of all things ITE when it comes to low voltage breakers. Their breakers are not just "compatible" with ITE, they ARE EXACTLY THE SAME breakers, they haven't changed in 25 years or more. There is no difference other than the company name.
They (Siemens) have documentation available to users and contractors for providing to AHJs, including the same thing for Murray (also Siemens). Getting that document can be difficult even if you use an official Siemens distributor (I used to be the guy that had and disseminated that letter, they eliminated my position), but if you buy from retail or surplus distributors, it will be impossible.