Add onion and pepper and cook, stirring frequently, until soft, about 5 minutes. Stir in sugar, vinegar, mustard seeds, and salt and bring to a boil. Add pears and cook until tender, about 5 minutes. Strain in a colander, reserve solids, and return liquids to saucepan. Over high heat, bring liquids to a boil and cook, uncovered, until thick and syrupy, about 12 minutes.
Return pears to saucepan and stir to coat.
Remove jars from water bath, let cool for 12 hours, and test for airtight seals. Label and store in a cool, dark place. If you decide not to sterilize and process jars, refrigerate chutney and serve within 3 weeks. Click here for more on The Proper Way to Preserve .