I remember what I was told to do with medicated shampoos. With medicated shampoos, you were supposed to squirt a palmful of straight shampoo into a cup or container and mix it with water (I don't remember the ratios). Then you pour the watered shampoo onto the dog and lather and let sit. I would suppose you do the same with tea tree oil. Just squirt a palmful into your hand and mix it with tea tree oil and water and lather it into your pup. Or, with homemade conditioner- you wash the pup and afterwards, you rinse the dog well. Then, you pour the homemade conditioner over the pup and dry off. Maybe you could use this method, but then...wouldn't your pup be kind of oily? LOL.

I know there are tea tree oil infused commercial shampoos out there, so I guess you could use the first method. Good luck! You might want to call your groomer.