Add the honey, sugar, water, tea bag, vanilla bean, and half the lemon thyme to a small pot. Bring to a boil. Let cook until sugar is completely dissolved, 2 to 3 minutes.
Meanwhile, divide the apricots and remaining lemon thyme between 3 pint-sized glass canning jars. Make sure they're packed in tightly. It'll feel like there's not enough room—don't worry.
Evenly pour the honey syrup over the apricots. Seal the jars, and process in a hot water bath for 10 minutes. Let jars cool before labeling, and storing in a cool spot in the kitchen or basement.