Add grated cucumber and salt to a sieve over a cup or bowl. Let sit for 5 minutes. Once the the cucumbers have released juice, stir or muddle to extract juice and set aside. Then add gin, dry vermouth and Castelvetrano olive juice to a mixing glass with ice. Stir for 30 seconds. Add cucumber juice and stir to combine. Finally, strain into two chilled martini glasses and garnish to your liking.