Simple answer: Asterik means you played with hard mode activated (turn it on by going to settings—the wheel like icon at top of screen). I recently learned about HM after playing 400+ games. None of my solved puzzles (NYT) ever had an asterisk. Ever since I’ve been playing HM, all my Wordle scores have the asterisk of honor.
https://www.reddit.com/r/wordle/comments/17zsgc9/what_does_the_asterisk_mean/

