Remove caliper bleeder screw, gently thread the hose or pipe from the grease gun in, not forcing it. You don't want to damage the threads. You will get a tiny bit of grease oozing out near that joint. Don't worry about it. Pump caliper full of grease forcing piston out. Scoop out the slug of grease, disconnect your grease gun. Wipe out as much grease as you can. The slug of grease not contaminated can be put in a small container for use on something in the future.
Brake parts cleaner sprayed in the caliper bleeder screw opening and caliper body will remove rest of the grease. Clean the groove for the caliper seal and replace the seal with a new one. Lube that seal with either brake parts assembly lube or red rubber grease or brake fluid.
If you are going to repaint the caliper for this before prepping the caliper for reassembly, of course...
You can cure the caliper paint on the bike if you don't have a small toaster oven you use for hobby stuff (don't use it to warm food anylonger!).