There is a YouTube video on this procedure which is excellent.
If the piston is all the way in, reassemble and use the brake hydraulic pressure to get as much as you can out. Then remove the caliper, separate the halves and, using a piece of tough rubber and vice grips work them off. Avoid damage to the cylinder! You can also go to a local garage or tire shop and ask'm to blow the cylinders out of the calipers. They come out easy with pressure applied to the pressure side of the caliper. Use the same caution as when opening a Champaign bottle. Use brake fluid and clean microfiber to clean everything. Use copious brake cleaner spray to clean channels. Use gloves. That stuff stings and skin. Order a set of Speed Bleeders. Feed new DOT 4 slowly from the top or buy a vacuum pump to suck the air out from the bottom. Brake fluid damages paint fast. Cover everything. Do not contaminate the new pads of rotors. Make sure your brakes hold before rolling the bike. Brake-in your pads. If you can fell groves on your rotors, you might need new rotors.
Triumph does not make a service kit for the calipers. They just sell the seals. Brembo might. I ordered mine from BrakeMasters. They are cheap and fit! Coat the seals and seal beds with the red grease in the kit. Once you are done you should have single finger stopping power.