Pre-heat grill to medium-high heat. Lightly brush the cut sides of the peaches with olive oil. Place the peaches on the grill, cut side down, and grill for about 3-4 minutes or until they have nice grill marks and are slightly softened. Flip and grill for another two minutes on the other side. Remove from the grill and let them cool slightly.
Once the peaches are cool enough to handle, chop them into small cubes. In a medium bowl, combine the grilled peaches, pomegranate seeds, red onion, jalapeño, and cilantro.
Add lime juice and a drizzle of olive oil to the mixture. Season with salt to taste and mix well. Serve the salsa immediately with tacos, grilled chicken, fish, or as a dip with tortilla chips.