Combine tequila and jalapeño in a bowl; let stand 2 to 4 hours. Pour through a small wire-mesh strainer into a bowl. Discard solids.
Place 2 tablespoons lime juice in a shallow dish. Stir together sugar, rind, and salt in a second shallow dish. Dip rims of 4 chilled 8-ounce glasses in lime juice then dip in sugar mixture.
Process infused tequila, honeydew, ice cubes, water, agave syrup, and remaining 3 tablespoons lime juice in a blender until smooth, about 1 minute. Pour evenly into prepared glasses.
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