Can Mucinex (guaifenesin) thin the mucus in my womb and thus endanger the fetus?

Minimal concern. Mucinex (guaifenesin) is guiafenesin, an expectorant-- a medicine to thin mucus so that it can more easily be cleared from the throat and sinuses. It is a pregnancy category c drug, so should be used with caution. There is no mucus is the womb to speak of, and there is no evidence that the presence or absence of cervical mucus has significance to fetal well-being.
No worries. Mucinex (guaifenesin) is safe to take. It will not cause any issue to you or your unborn.