Lewis & Short

Thyrē, ēs, f., = Θύρη, a little town in the Peloponnesus, the possession of which was contested by the Argives and the Lacedæmonians, Stat. Th. 4, 48.
Hence, Thy-rĕātis, ĭdis, adj. f., Thyreatic: terra, the region of Thyre, Ov. F. 2, 663.