The idea of blood being mingled with their sacrifices should be understood as the Galileans being killed when they came to Jerusalem and made offerings at the Temple, whether or not they were actually killed in the Temple precincts. Indeed, Galileans may have come to Jerusalem for political purposes as well as religious ones.
Josephus relates an episode in which Jews of Caesarea (most of whom would be Galileans) confronted Pilate in a life-risking demonstration opposing his having brought Roman ensigns of Caesar (golden eagles) to Jerusalem. Following this, Pilate brutally suppressed a related demonstration in Jerusalem itself.
After this he raised another disturbance, by expending that sacred treasure which is called Corban upon aqueducts, whereby he brought
water from the distance of four hundred furlongs (50 miles). At this the
multitude had indignation; and when Pilate was come to Jerusalem, they
came about his tribunal (court), and made a clamour at it... Now the Jews were
so sadly beaten, that many of them perished by the stripes they
received, and many of them perished as trodden to death by themselves...
Galileans already stirred up because of Pilate's bringing Roman standards to the holy city, would certainly have joined or even led these demonstrations. So this may be the episode that the OP refers to. However, there are other possibilities. Acts 5 tells of the Zealot leader Judas the Galilean.
Acts 5:36-37
Some time ago, Theudas appeared... After him
came Judas the Galilean at the time of the census. He also drew people
after him, but he too perished and all who were loyal to him were
scattered.
Although this Galilean's rebellion took place earlier than Pilate's reign, his sons continued to act against Roman rule. According to Josephus, two of his sons, Jacob and Simon, were crucified by Tiberius Alexander, a later Roman procurator of Jewish birth. Another son, Menahem, became the leader of the Sicarii. Josephus does not report that Pilate was involved in putting down these rebellions but this would be a logically possibility since the Galilean's sons continued his work until well after Pilate left the scene.
It should also be mentioned that Pilate was finally removed from office for reacting too harshly to a possibly messianic movement among the Samaritans.
Pilate's last deed of cruelty, and the one which brought about his
downfall, was the massacre of a number of Samaritans who had assembled
on Mount Gerizim to dig for some sacred vessels which an impostor had
led them to believe Moses had buried there.
Conclusion: Pilate brutally suppressed what he perceived as threats to Roman rule in Judea, sometimes involving factions that must have included substantial numbers of Galileans. It is not possible to say with certainty which of these Luke 13 refers to. However, the deaths of Jews protesting his use of temple treasure for the system of Roman aqueducts is a likely candidate. The repression of the movement begun by Judas the Galilean is another possibility.