Q - During Mass, why is the Kyrie Eleison (Lord, have mercy) the only part of Mass in Greek when everything else is done in Latin or the local language?
A - Thanks for the question. To be precise, we also have some Hebrew in our Mass, including Amen, Hosanna, and Alleluia.
Yet, the Kyrie is the only part of Mass in Greek and it means "Lord have mercy". In most places, it is said or sung in the vernacular, but can also be done in Greek.
A bit of history might help answer your question. The Kyrie pre-dates Christianity, and there is no record of it being used in the liturgy until hundreds of years after Christ. It seems that the first mention is in the Eastern Churches sometime in the 4th century. The first evidence of it being used in Western Churches is the 6th century.
Thus, the Kyrie entered the Western Mass much later than in the Eastern liturgy and was introduced, most likely, because it became popular as a litany, which was sung in Greek in the East and then kept the same form when it moved to the West. Thus, the popularity of it kept it in Greek, rather than changing it into Latin.