People Magazine published this article making the claim that, "Getting a tattoo, regardless of size, increases the risk of developing lymphoma by 21%, according to a new study"(https://people.com/tattoos-increase-risk-of-developing-lymphoma-by-21-new-study-finds-8654298). The study in which this supposed information was received comes from sciencedirect.com which is not a government source and has been known to make some mistakes in their articles. However, overall this site is more reliable.
The obvious misinformation here comes from People Magazine's mistranslation of the information derived from the ScienceDirect article. In the scientific findings, the number 21% comes from the number of people in the experiment who had tattoos. The author of this People Magazine article takes this 21% and labels it as how much more likely an individual with tattoos is to develop lymphoma cancer. Based on the numbers given by the report, it seems like individuals with tattoos are 3% more likely to develop lymphoma (https://www.sciencedirect.com/science/article/pii/S2589537024002281).
The same data can be found in a publishing by The National Library of Medicine, stating that those who had more recently gotten their first tattoo (specifically within two years) had a higher risk of developing lymphoma. Additionally, the findings state that there is no evidence that a larger tattoo would increase the risk of developing lymphoma (https://pubmed.ncbi.nlm.nih.gov/38827888/).
The final interpretation does not claim how much more likely someone with tattoos is to develop lymphoma cancer, rather, it simply claims that there appears to be a correlation of the two. The article even claims that it is not definite and that further research and experiments are needed.
Overall, the information provided from the science journal was misinterpreted and therefore, the claim is actually false. Overall I would categorize this claim as exaggerated and misleading, as there appears to be some truth in it.