Even the authors agree with awestley:
> Additionally, having a tattoo, especially among adolescents, has been suggested as an indicator of risky lifestyle highly associated with e.g. smoking [4] and alcohol consumption [46] – both risk factors of certain cancer types. Hence, evidence of an association between tattoo ink exposure and occurrence of cancer may be confounded by other health-related lifestyle factors. We intend to exploit the remainder of the information gathered in the survey in the future.
Indeed, it does seem like a big problem that should really be accounted in the initial analysis.
You could also look at tattoo coverage, as in how much of the body is covered in ink? Would a small tattoo on the shoulder have as much risk as a full back tattoo? There are a lot of extra confounders here that could be better explored, but it gets difficult to get a full dataset. However, given their survey data, they should have more analysis options with more time.
The lack of confounder analysis is a bit surprising, but perhaps the paper was long enough already.