There are epigenetic effects - environmental effects on genetic material - that are passed on to offspring. Some are obvious - exposure to radiation or mutagens - increases the likelihood of genetic defect diseases in children of parents who were exposed.
Another effect is the apparent DNA effects found in mothers and offspring living after a famine
http://www.bio-medicine.org/medicine-news-1/First-evidence-that-prenatal-exposure-to-famine-may-lead-to-persistent-epigenetic-changes-28269-1/
So this does indicate that while envrionment can damage DNA, learning in and of itself does not damage DNA.