Combine green tomatoes, sugar, raspberries, and jalapeno peppers together in a saucepan; cook and stir until sugar is dissolved and raspberries and tomatoes are broken down, about 15 minutes. Remove saucepan from heat and stir in gelatin mix until well blended.
Pour tomato-raspberry mixture into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth.
Sterilize the jars and lids in boiling water for at least 5 minutes. Pack tomato-raspberry mixture into hot, sterilized jars, filling to within 1/4-inch of the top. Run a knife or thin spatula around the insides of the jars after they have been filled to remove any air bubbles. Wipe the rims of the jars with a moist paper towel to remove any food residue. Top with lids and screw on rings.
Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars into the boiling water using a holder. Leave a 2-inch space between the jars. Pour in more boiling water if necessary to bring the water level to at least 1 inch above the tops of the jars. Bring the water to a rolling boil, cover the pot, and process for 10 minutes.
Remove the jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart, until cool. Press the top of each lid with a finger, ensuring that the seal is tight (lid does not move up or down at all). Store in a cool, dark area.
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