That looks like a steel rivet. I would use a diamond ball burr and
gently grind the heads down. Take your time. When you get the
circumference of the heads thin enough, use a very sharp burnisher
and pry up the edges all the way around. Don’t use the sterling tips
as a fulcrum as they will be damaged. Continue to grind away at the
rivet and eventually only the rivet shaft will be left. Soak the
entire tip with leather intact in some WD-40 for 1/2 hour, then
remove the tip and wipe off excess WD-40. Now drill a hole in a piece
of hardwood slightly larger than the rivet shaft. Place the sterling
tip so the shaft is directly over the hole you just drilled, then
drive out the rivet.
The wood will support the tip from deforming. The leather should
pull right out.