How do teratogens change your genes?

They usually don't: Teratogens (from terata or monstrosity) are agents that act on the developing embryo/fetus to cause birth defects. Known mechanisms include interference with molecules that govern limb, brain, heart formation like thalidomide or Methotrexate (a folate (folic acid) inhibitor). Teratogens usually affect only the exposed pregnancy and do not change the genes of mother/fetus for future pregnancies.

Teratogens and DNA: Teratogens are toxic exposures that adversely affect a fetus, such as certain chemicals, drugs/alcohol, medications, or X-rays. While ionizing radiation could cause mutations in the mother or developing baby, most teratogens act without directly altering the DNA code. Some teratogens cause epigenetic changes, which influence how genes are expressed, but don't change their sequence.