Rabbi Brant Rosen writes addressing this question.
Being omniscient, wouldn’t God automatically know the difference between an Israelite and an Egyptian house? Rashi answers this question by pointing to the words “a sign for you.” According to this interpretation, the blood on the door post is less a sign for God than it is for the Israelites - presumably as a reminder of God’s redemptive power.
After addressing the classic sources, Rabbi Rosen brings two "post-scripts" which are powerful applications of the need we have to mark, make concrete evidence of our ability to survive. Read it.