I always thought “American Graffiti” was one of the influences.
Grease was more memorable to me because my sister was always playing the record, singing the songs, and going to the movie. When I looked up Grease, I found that Sha-Na-Na was an influence on that, and I took it from there. There was a leather jacket guy in American Grafitti, but the comic aspects of Fonzi may owe more to Bowser or Grease.
You're right, though. However big Grease the movie would be later, more people saw American Grafitti than Grease the musical, and Marshall must have seen it too.