In regards to tannins in tea, there really is a mixed bag of effects. Yes, tannins interfere with iron absorbtion, but it takes "excessive" tea consumption to really have an effect on the iron. It's a reaction that happens when the tannins an iron "meet" in the digestive tract where the tannis bind to the iron, and can prevent it form being absorbed as fully as it would be without the presence of the tannins. If there's no iron present at the time, there's no problem. And, adding milk to tea neutralizes the interaction of tannins and iron, as does adding a couple of drops of lemon juice to your tea.
Tannins are only released from tea after it has seeped longer than 2 minutes in boiled water - so if you take your tea bag out of the water before that, your tea will be relatively tannin free.
Tannins are what is responsible for tea's many benefits - tannins have antiviral and antibacterial properties and they are also what is responsible for tea calming you and relaxing you. In terms of the antibacterial properties, tea can also help to fight gingivitis and gum disease.
So, milky tea seeped for less than 2 minutes = not enough tannins to bat an eye at!!!