Bring garlic and vinegar to a boil in a 2-quart saucepan; reduce heat, and simmer 15 minutes. Pour into a glass bowl; cover and let stand 24 hours.
Pour vinegar mixture through a wire-mesh strainer into a 1-cup glass measuring cup, pressing garlic with the back of a spoon to squeeze out liquid; discard solids.
Bring vinegar mixture, 3 cups water, and pectin to a boil in a 5-quart saucepan, stirring constantly. Add sugar; return to a boil, stirring constantly. Add oil; boil, stirring constantly, 2 minutes. Remove from heat, and skim off foam with a metal spoon. Add food coloring, if desired.
Pour hot jelly into hot, sterilized jars, filling to 1/4 inch from top; wipe jar rims. Cover at once with metal lids, and screw on bands.
Process in boiling-water bath 5 minutes. Use on grilled chicken, pork, and lamb.