I am sorry to hear you are worried about Lady. I am a veterinarian, and will do my best to help.
Tea Tree oil is toxic
to dogs if taken internally or if absorbed across inflamed skin. You must not be using much since you have not seen a problem, but dog have become temporarily paralyzed from having tea tree oil applied to the skin:
Chewing the feet can be a sign of an allergy to something in the environment, like pollen or dust or things in the home.
You could try something distasteful like Bitter Apple or Bitter Orange.
Antihistamines like Benadryl and Claritin might help. How much does she weigh? Benadryl is 1 millgram per pound of body weight 2 to 3 times daily; Claritin is about 5 mg once daily.
There are supplements that might help: nettles, fish oil, quercetin, vitamin E, anti oxidants, probiotics.
Topical cortisone ointment might help.
Let me know what else I can help with or answer.