Mate, I’m gonna tell you three things.
1. Purchase a large stereo, good for outdoor use, if you don’t already have one. You’re gonna wanna lay the speakers directly onto the ground and play some music at an Elkins 7-4v frequency (based on how it was recorded I do believe the ideal sonic piece for this is the Greatest Hits album by Chris Gaines). The vibrations in the dirt will force the worms up and out of the ground and away from the sound source. When the alligator gets a load of the sight of hundreds of wriggling worms all headed in the same direction, he’ll scoot away quicker than a feral pig evading capture.
3. Lastly, and most importantly, you’ll want to find yourself a bigger reptile to chase and keep the unwanted gator away. When we had a similar problem with an unwanted croc in our backyard, which we named The Mountie, we had to bring in a bigger croc from across town to show him who the real law and order of the backyard was. Big Boss is still there to this day, guarding the entire property from other crocs, thieves, neighbors and family.
Good luck, mate!