Heat vinegar, water, and salt in a saucepan over medium-high heat; bring to a boil. Remove from heat.
Sterilize jars and lids in boiling water for at least 5 minutes. Pack okra, 1 pepper, and 1 garlic clove tightly into each of the hot, sterilized jars; sprinkle mustard seeds over the top. Pour vinegar mixture into each jar, leaving 1/2-inch space at the top. 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. Once 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, and wait at least 4 weeks before opening.