Its best to remove the complete carrier,give the slider a good soak in plus gas, or very thin penetrating oil, and then lock the square section of the pin end in a vice,a bit of localised heat with a small butane torch will help too, then gently, and i mean VERY gently move the calliper side to side until it breaks the seize.
They snap easily though so be careful.
Clean the inside of the slider and pin with a fine emery paper and re grease with a proper rubber grease (red in colour) and make sure the rubber gaiter is properly seated otherwise it will let corrosion back in.
hth 😉