This is a Phase 1 B feasibility trial with Galunsertib, a TGFβ inhibitor, in combination with carboplatin/paclitaxel in patients with newly diagnosed, persistent or recurrent carcinosarcoma of the uterus or ovary. The objective of the study is to determine whether this drug combination is safe for this patient population and to see if it is effective in shrinking cancers, keeping them from growing or helping patients live longer.