Bring pears to a boil in a large stockpot over medium-high heat; cook until tender, about 20 minutes. Drain; cool. Peel, core, and coarsely chop.

Combine chopped pears, onions, bell peppers, and jalapeños in the bowl of a food processor; pulse until finely chopped.

Transfer pear mixture to a large pot over medium-high heat; stir in vinegar, sugar, mustard, and salt until well combined and bring to a boil. Reduce heat to medium-low; simmer until flavors are blended and relish is thickened, about 1 hour.

Meanwhile, inspect 10 pint-sized jars for cracks and rings for rust, discarding any defective ones. Immerse in simmering water until relish is ready. Wash new, unused lids and rings in warm soapy water.

Pack relish into hot, sterilized jars, filling to within 1/4 inch of tops. Run a clean knife or thin spatula around insides of jars to remove any air bubbles. Wipe rims with a moist paper towel to remove any residue. Top with lids and screw rings on tightly.

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 20 minutes.

Remove jars from the stockpot and let rest, several inches apart, for 12 to 24 hours. Press centers of lids with a finger to ensure lids do not move up or down. Remove rings for storage and store in a cool, dark area.