Get a FACTORY rebuild kit. (Hint: there are no Mazda/ATE/Aisin factories in Mexico) ;)
Pull the caliper off...plug the brake line fitting. Don't retract the piston first. The fluid in the calipers is the nastiest stuff in your brake system. Don't press it back up the brake hose if you are going to rebuild anyway.
First...clean the outside with a wire brush then brake cleaner. Once it's dry, paint it. Since you're replacing the boot, you don't have to worry about masking anything.
Then stuff a rag in front of the caliper and apply a little bit of compressed air with a blow gun...just a little, because that sucker will leave the caliper at terminal velocity.
Rip off what's left of the boot and then take a pick or a knife and remove the old retaining ring.
Clean the bore with a clean rag soaked in clean brake fluid.
Replace the o-ring on the caliper. It should be lubed with the pink moly soap that is included in the rebuild kit.
Put a little bit of brake fluid on the new retaining ring, and work it around the boot until it seats...it's a little fiddly, but you'll figure it out. No tools, you'll rip the new boot.
Done. Bleed it good.
This is one of the best ways to spend $50 on a used car.