One of the Met Police officers allegedly sent a message to Wayne Couzens about tracking down a girl.
The charges are denied by William Neville, 34, Jonathon Cobban, 35, and former PC Joel Borders, 45.
Couzens is serving a life sentence for kidnapping, raping, and murdering Ms Everard in March of last year.
Prosecutor Edward Brown QC said of Neville, from Weybridge, Surrey, “He got pleasure from the detention of a 15-year-old girl with what he called a’struggle snuggle.'”
“We contend that this is a rape fantasy.”
“Cobban encourages this with a ‘haha’ and an amused reaction.”
According to Mr Brown, the phrase “struggle snuggle” refers to “using lawful physical restraint as an excuse or cover for non-consensual physical or sexual contact.”
Other messages, allegedly sent in the group two years before Couzens killed Ms Everard, were read aloud in court by Westminster Magistrates.
Cobban, from Didcot, Oxfordshire, made a comment about domestic violence victims.
Mr. Brown stated that the messages “target the most vulnerable members of society, who frequently feel unable to report abuse to police.”
Meanwhile, Borders, of Preston, Lancashire, is accused of discussing raping a female coworker.
Cobban stated in police interviews that he regretted sending the messages, calling them “stupid.”
Borders described his remarks as “dark humour that I understand will offend some people.”
The three officers were previously with the Civil Nuclear Constabulary before joining the Met on February 11, 2019.
Cobban and Neville, both 34, are police officers who are currently suspended.
The three men have been charged with violating Section 127 (1) of the Communications Act of 2003, which deals with “improper use of a public electronic communications network.” The messages’ content is said to be “grossly offensive.”
The three men do not deny sending the messages, but they do deny being grossly offensive.
Due to other ongoing investigations, Couzens’ messages were not read in court.
The trial is still ongoing.