From Georgetown's Booster Site - also mentions GMU-Georgetown
Another Reason/Need for the DMV Invitational
GMU - GWU - GT - Maryland - Howard - American - UMBC - Va - VaTech - Richmond
on some type of rotating schedule
40 Years Of DC's "Cold War"
6/9/21

"A total of 6,800 feet separate the borders of Georgetown University and George Washington University, but it may as well be a thousand miles."
That's a quote from the Georgetown Basketball History Project in 2018 on the state of relations between these two local universities, which have not met on the hard court in 40 years. Academically and athletically, it's as if the two schools barely acknowledge one another.Athletically, GW sponsors every sport Georgetown does except football, field hockey, men's lacrosse, and women's golf. Matchups between the Colonials and Hoyas are common in sports such as baseball and tennis, but men's basketball remains at a visible impasse: the most recent meeting between the schools was 1,495 games ago.
In the 93rd game of the series, Georgetown defeated George Washington, 61-48, on December 16, 1981, before 8,695 at Capital Centre during Patrick Ewing's freshman season. The series was not renewed in 1982-83 and neither school has proffered the cause for the decision. In 2006, the GW Hatchet newspaper stated that "GW's athletic staff, which formulates the schedule, decided to end the series for unknown reasons."
When Ewing held his introductory press conference as head coach on April 6, 2017, the second question he faced was from the late Mark Plotkin, asking Ewing if he would support a proposed "Ward Two Classic" between the schools.
"That is something I'm not at liberty to discuss right now," Ewing said. "That's something that Lee {Reed] and I would sit down and discuss when the time is appropriate", and it's the last time Georgetown has publicly discussed it.
There are many suspects in these battles (old feuds, scheduling disputes, gate revenues, the demise of the BB&T Classic, etc.) but no single culprit; regardless, in the last 10 seasons Georgetown has scheduled a grand total of three home games with Howard, two with American, one with Maryland, and none with George Washington. (This doesn't even begin to explain why Georgetown and George Mason do not play. The Hoyas played at GMU in December 1985, and the Patriots never returned a game since.)
While Georgetown will be filling out its 2021-22 home schedule this summer with the likes of Radford and Maryland-Eastern Shore amidst empty seats at Capital One Arena, these nearest of neighbors continue to ignore each other.