According to the CTR instructions, the ITIN is acceptable:
Item 6. SSN/ITIN or EIN. Enter the Social Security Number (SSN) or Individual Taxpayer Identification Number (ITIN) or Employer Identification Number (EIN)of the person or entity identified in Item 2. If none, write NONE.
Specifically, what reason are they giving you for kicking the CTR back?
It may be that the ITINs you are being provided are simply "composed" on the spot. All the offeror would have to do is come up with a nine digit number beginning with a "9" unless you require a copy of the letter from the IRS awarding the number.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.