Proselutos (προσήλυτος) means a proselyte — a Gentile who had converted to Judaism, accepting circumcision (for men), Torah observance, and full identification with the Jewish people and their God. The word derives from proserchomai (to come toward/approach) and describes one who has 'come over' to another faith and people. It appears in Matthew 23, Acts 2, 6, and 13.
Proselutos in Matthew 23:15 is the target of the Pharisees' evangelistic zeal — yet Jesus says they 'travel over land and sea to make one convert, and when you have succeeded, you make them twice as much a child of hell as you are.' The issue is not conversion but what they are converted to. In Acts 2, proselytes were among the Pentecost crowd. In Acts 13, Paul preaches to both Jews and proselytes — pointing to Christ as the fulfillment of what the proselyte was seeking.
The proselyte was someone who 'came toward' (proserchomai) the God of Israel from outside. The New Covenant removes the barrier: in Christ, there is no longer the need for the proselyte category. Gentiles are not 'converted to Judaism' but grafted into Israel's root (Romans 11) through faith in Israel's Messiah. The proselutos institution was a shadow of the universal gospel.