Take the peeled peaches and place them a blender or a container into which an immersion blender can fit. Puree the peaches smooth and measure out two cups of puree.
Put the mustard seeds in a dry skillet and toast them for 1 to 2 minutes, just until they start to pop. Transfer them to a plate to cool. Once they're cool, put them in nested resealable bags. Close the bags tightly and crush the seeds using a rolling pin or heavy-based bottle.
Pour the peach puree into a small saucepan and add the crushed mustard seeds, sugar, lemon juice, vinegar, and salt and stir to combine.
Cook, stirring constantly for 5 to 7 minutes, until the mustard begins to thicken.
To can, funnel mustard into hot jars, leaving 1/2 inch headspace. Wipe the rims, apply lids and rings, and process in a boiling water bath canner for 15 minutes.
When the time is up, remove the jars and set them on a folded kitchen towel to cool. When the jars have cooled enough that you can comfortably handle them, check the seals. Sealed jars can be stored at room temperature for up to a year. Any unsealed jars should be refrigerated and used promptly.