the Gospel writers only clearly show relating the story to the OT and not, say, to mystery Greco-Roman religions or Homeric epics.
In general this is true but there are some instances in the NT where we can see the influence of Homer. The most obvious example I know is the story of Eutychus in Acts 20 being a transvaluation of Elpenor in the Odyssey.
That's really a stretch. The only link between the two is that both prefigured Humpty Dumpty by taking a great fall. Tho obviously the tale of Humpty Dumpty was more influenced by Elpenor than Eutychus since like Elpenor, Humpty Dumpty was not put back together again.
The reasons why they fell, their end fate, and their use within the narrative were completely different. It's a fevered take from a grad student desperate for a thesis topic to satisfy a professor who thinks much of the New Testament was a response to the Homeric tradition.