Summary:
There is no concrete evidence that proves that drinking caffeine while pregnant causes deformity. My sources explained how caffeine could cause more subtle side effects such as increased heart rate or disruption of fetus growth; however, there is no direct proof that drinking caffeine leads to deformity. Additionally, the National Library of Medicine goes even further and explains how drinking caffeine while pregnant in moderation actually has no effects whatsoever on a pregnancy. They even state how 70% of women admit to still consuming caffeine while pregnant. The American Pregnancy Association agrees with the National Library of Medicine by also explaining how caffeine could cause side effects but only when it comes to extremely high intakes. So, overall, there has been no evidence that supports this exact claim.
Sources:
https://americanpregnancy.org/healthy-pregnancy/is-it-safe/caffeine-and-pregnancy/
https://pmc.ncbi.nlm.nih.gov/articles/PMC10625456/