The main concern for extracting tannins is during a sparge. In sparging, my understanding is that three conditions must be present to extract tannins - 1) pH >6, 2) temp >170F, 3) runnings gravity <1.010. Squeezing a bag could be considered a kind of sparge since you are pushing additional wort out of the grain. Whether or not that is an accurate characterization, I'm not sure. It seems not since you're squeezing wort out, not adding new fresh water to rinse the grains.
However, even if it could be considered a sort of sparge, it would be highly unlikely that the three conditions above would be met. The temp of the wort you squeeze out will be about the same as your mash temp (i.e. <170). The pH will be pretty much the same as your mash (i.e. <6). As for gravity, I've measured the gravity of the "squeezings" and they have always been well above 1.010.
In other words, squeeze it until it begs for mercy.