Good morning. Long time reader first time contributor here :) Thanks for funneling us these brain challenges, Sujit!
Below my best attempt at the confounding triangles, though I am not confident about the proxy approach proposed by Elizabeth Cook.
No, I do not think that teen pregnancy can be considered causal - although they did control for income, education, and pre-existing health problems, I feel there are just too many unmeasured (or unknown!) confounders at play to make a causal inference. Association at best. Some confounders that I think should have been considered include: ethnicity (considering influence of systemic racism on health behaviours and health outcomes), history of abuse, and history of undiagnosed health (specifically mental health) conditions - as the only thing the cohort data would have captured is conditions for which people sought use of the health system).
As a next study, maybe a case-control study could be used. This would allow for the collection of a wealth of info on hypothesized confounders. However, it would be prone to recall bias and would also be dependent on using proxy respondents (at least for the cases) which may threaten the internal validity. Maybe there are known genetic links to teen pregnancy and we can do a Mendelian Randomization (he...he...). @Epi-colleague - any better ideas?