The trick is to properly crack the eggs before marinating. When you crack the eggs, make sure that the membrane underneath the shell is broken as well. So the marinating liquid goes in between the membrane and the eggs. This way the eggs will be more flavorful, and it will become easier to peel afterwards.
The other thing is the freshness of the eggs themselves. The fresher the eggs, the harder to peel later.
The other trick is when you soak the eggs in the ice bath, start to very quickly crack all of them while they submerged in the ice water. It helps the membrane to be more detached from the eggs, resulting in easier to peel eggs later.

You can use something very generic like Lipton. Because the other ingredients (soy sauce etc) are quite strong, so the tea doesn’t have to be a very special one. I usually use black tea, but you can experiment with different types of tea such as pu’erh as well.

You don’t need super fancy black tea. The regular tea bags will work.