Your lungs breathe, your heart beats, your mind thinks. When your mind is thinking thoughts, it's just doing what it does, according to its nature.
You have hands, ears, toes, but you are not your hands, ears, toes. Your mind is another part of you. You have a mind, but you are not your mind.
You can ignore your breath. You can observe your breath. You can influence your breath. The same goes for your thoughts. You can observe thoughts, or you can ignore them.
Thoughts will come and go. Let them. And then enjoy your tea in quiet.