Definitions of third country
(of migration) a term used to describe a country which is not a person's country of origin but which a person is applying to enter from another country which is also not that person's country of origin. For example, if a British national living in America applies for a visa to enter Russia, then Britain is the home country, the US is the host country, and Russia is the third country.
We can't send him to a third country. He needs to be sent back to Turkey.
a country that is not a member of the European Union
The UNHCR also specifically asked Britain to suspend application of the safe third country rule in the case of Yugoslavs.