Tapping the rivets snug may or may not work as Bill said. It also may split the scales. If a new handle isn't what you want to do, try making this one more secure.
Mix up some thin epoxy and work it under the scales with gloved hands where the scales have lifted. Work in some fine dark sawdust after the epoxy gets in. Wipe the excess off the scales with denatured alcohol, and do that again after the resin has gelled. Let it dry and lightly sand the handle by hand as needed.