Eagan, who was elevated from the practice squad after the Giants lost receivers Odell Beckham Jr, Brandon Marshall and Dwayne Harris to season-ending injuries in Week 5, had been the punt returner.
He appeared in four games for the Giants, but did not have a reception on offense. He returned four punts for 20 yards, the 20 yards coming on his first punt.
Raymond, 5-9, 160 pounds, has previously played for the Broncos and the Jets. In six career NFL games, Raymond has returned 16 punts for 149 yards (9.3 average), and has four punt returns of 20 or more yards to go along with four career fumbles.
Raymond, who also has nine career kickoff returns for 222 yards (24.7 average), does not have a regular season reception on offense.