The extra galactic probe was a probe sent to the Milky Way Galaxy from outside the galaxy. Sometime prior to 2364, the USS Greyhound encountered the probe. The location of this incident was marked in viewscreen readouts aboard the USS Enterprise-D on several occasions in 2364, in the form of star charts from the Enterprise library computer. (TNG: "The Last Outpost", "Datalore", "Conspiracy")
According to Spaceflight Chronology, (pp. 115, 121) the encounter was not a recent event, but a historic one. It had occurred during the era of deep space exploration fifteen years after the Earth-Romulan War had ended. The encounter was the first evidence found that extragalactic life existed. The probe dropped out of warp 10,000 kilometers away from the Greyhound. The probe itself could not be analyzed by the crew, but the ion trail of the probe indicated that it had been traveling at a speed of warp 30, and had originated from the Small Magellanic Cloud.