Strain the liqueur, first through a mesh strainer or chinois, then through a coffee filter. The finished product may still be a bit cloudy, but the small amount of particulates won’t affect the flavor. The liqueur can last indefinitely, and will eventually settle out.
Spicy Variation: If you want something that tastes a bit warmer, trade the lime peel for lemon peel, and the regular sugar for brown sugar. When pouring in the jar, add two cinnamon sticks, five crushed allspice berries, and four cloves, then steep as before. Strain out all the spices when done.
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