Lightly brush the watermelon slices with vegetable oil and season with salt. Arrange on the grill and grill until you have visible grill marks on both sides. Remove the rind and chop the flesh into large chunks. Add the watermelon flesh to a blender, along with 1 cup of water and blend until liquefied. Strain the juice, through a fine strainer, into a bowl. Discard the pulp and reserve watermelon juice.
In a large bowl or glass pitcher, combine the tequila, simple syrup, lime juice and watermelon schnapps. Add the grilled watermelon juice, and stir. Pour into serving glasses and garnish with reserved slices of grilled watermelon and a jalapeno pepper.
Jalapeno Infused Simple Syrup:
In a small saucepan over medium heat, add the water, sugar and the jalapeno pepper. Heat the mixture until the sugar is dissolved, about 2 to 3 minutes. Remove from the heat and let steep until cool. Remove the pepper slices and reserve the simple syrup.