Tea tree oil would be CONTRAINDICATED on a BF mom's nipples.  Although it has
its uses as a treatment for skin conditions, it should not be used
internally.  The risk of the infant ingesting tea tree oil from mom's nipples
would contraindicate its use.  When taken internally, even small amounts of
tea tree oil can produce neurologic toxicity including confusion, muscle
weakness, and tremors.  Tea tree oil can also cause contact dermatitis if
applied to broken skin.
Source:  Kemper, Kathi J., MD, MPH  "Seven Herbs Every Pediatrician Should
Know" in Contemporary Pediatrics, Vol. 13, No 12, December 1996, pg. 79 ff.
Hope this helps.
Linda Shaw MD