If the US collects the data in a different way and then doesn't publish anything else, there is no other data available. All you can do is include a note that explains why the numbers aren't comparable.
Sorry, the 'should' probably has an unintended negative connotation when talking about a specific study.
To delve a little deeper. They seem aware (under HOW WE CONDUCTED THIS STUDY [1]): "While the information collected by the OECD reflect the gold standard in international comparisons, it may mask differences in how countries collect their health data. Full details on how indicators were defined, as well as country-level differences in definitions, are available from the OECD."
They do not mention the specific CDC caveat mentioned above regarding the check box on US death certificates.
And then the pincher: The study points to CDC [2] where explicitly this effect is mentioned as a possible issue with the reporting via death certificates ("Efforts to improve data quality are ongoing, and these data will continue to be evaluated for possible errors.").
I'll leave the interpretation to you. They mention there is a gold standard and that some countries might not follow that gold standard. The conclusion is mainly based on US CDC data vs. OECD non-US data. They link to a CDC report mentioning this issue. Should they mention this fact in the study in the main body, or is this transparant enough?
Going back to the Noahpinion link with graph above in this discussion. For me the time series gives quite the hint that ICD-10 is not being followed appropriately and that false conclusions may arise. If this were my report, I'd take one or two paragraphs to explain why this issue doesn't affect my conclusions in the main body of text.
And then even a 'How to solve this (partially)'. As an actuary I know death is very unlikely in the childbearing age. Show a comparison table of deaths per 100k for women in the age of 20-40 between countries, including the 'US-Black' category. If that comparative line is a lot more flat (my expectation), I would really presume there is a data collection issue. The other interpretation would fail Occam's razor (that non-pregnancy death in US / US-Black categories are less likely than in other OECD-countries). First inkling: [OECD - 3], US ASMR in Women up to 20% higher than other countries.
Do you have some evidence they didn't?