Well - drinking "true tea" with high fat meals can actually help out with breakdown. However, if you're eating a salad or any meal with a high-intake of non-heme iron (from plants), the tannins in tea will effect the absorption rate.
Since most of us aren't vegetarian or vegan we can drink as much tea as we want before, during and after our meals. (Provided heme iron is present).
Tannins in tea chelate non-heme iron. They form an insoluble bond with some of the iron molecules making them indigestible.
Drinking teas an hour before or after helps reduce the inhibition of non-heme iron absorption.
So realize what you're eating, and decide whether to drink tea with your meal or not. If you have cereal, legumes, or leafy greens planned for consumption, merely avoid the tea for an hour.
We know vitamin C is found in teas, along with some other acids, and may aid in non-heme iron absorption, and even counteract some of the static interference caused by tannins. It does this by adding an electron to the iron molecule, changing it from its ferric form to ferrous, making it easier to digest. Therefore a little lemon in your tea goes a long way.
Also, I'll admit, a splash of milk in your tea can help bind tannins to the calcium molecules, instead of non-heme iron molecules (which we want).
However, I'd rather just drink it separately.
Hope this clears things up a bit.