Giardia is spread by fecal contamination.  There is no way the bugs can migrate from the gut to the breastmilk inside the mother's body.  Scrupulous handwashing prevents spread of infection between family members.  Breastfeeding will also confer immunity on the child, as maternal antibodies appear in milk.
Over 15 years ago I had a giardia infection which required treatment.  The public health authorities who monitored outbreaks of giardia informed me that children in daycare were the most common reservoir of infection, and often had no symptoms themselves.  I had a child in daycare who was two and a half at the time.  She was also breastfed, which may well be why she never developed symptoms.  This was before I knew about the wonders of the human immune system which prioritize antibodies to the breastfed child.
The treatment I received was contraindicated for infants and breastfeeding mothers of infants.  In view of the fact that my breastfed child was herself old enough to be treated with the same drugs if that had been necessary, I chose to take the treatment and not worry about it.  If I recall correctly, the treatment was two doses 12 hours apart.
If this mother is without symptoms, I suppose she could choose not to treat her bugs.  In my case it was out of the question as I was so dehydrated that breastfeeding would have had to stop for that reason.
Most parasites have a very specific and convoluted route from host to host, often involving more than one vector.  Some diseases can be transmitted in any bodily fluids.  Protozoans are large critters, microbially speaking, and don't cross epithelial barriers easily.
On the up side, it was the most effective rapid weight loss method I have ever experienced.  Unfortunately I didn't need to lose 10 pounds at the time, and now that it would come in handy, I don't have a child in daycare any more.
Rachel Myr

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