Borer - Removing a Tea Bag from the Liquid

I sent the following question to Rav Ostroff:

Siman 319:9 (It is forbidden to put dregs inside a strainer even when the strainer was hanging before Shabbos, but if the dregs were put inside before Shabbos it is permitted to pour water over them until the water becomes clear) seems to describe perfectly a tea bag. Clear water goes into the bag, picks up the flavour of the tea from the leaves and then drops through the other side. So why is it assur to take a tea bag out and let it drip back into the cup?

Rav Ostroff replied:

The difference between the two is that in the first case you are pouring water, which does not require separating (that's the explanation we gave), and [in the second case] you are lifting out the tea bag in order to separate the leaves from the surrounding beverage.

For further discussion see SSK 3:48 footnote 171 and Sefer Shulchan Shlomo siman 319 paragraph 2.