Begin by preparing your workspace to protect it from debris and cleaning agents. Lay down an old towel or rag in the sink basin and on the countertop around the work area. This will catch any putty flakes and prevent scratches. Most importantly, put on your safety glasses to protect your eyes from small, sharp pieces of hardened putty that can fly off during removal.

Take a plastic putty knife or a similar non-marring scraper. Start by gently chipping and prying at the edges of the hardened putty ring. Because it's old and brittle, large chunks may break off easily. Work your way around the entire circumference. The goal here is to remove the bulk of the material without applying excessive force that could damage the porcelain surface. Do not use a metal tool at this stage.

To deal with the stubborn, bonded putty that remains, you'll need to soften it. Use a standard hairdryer on its highest heat setting, or a heat gun on its lowest setting. Hold the heat source about 2-3 inches from the putty and move it continuously in a slow, circular motion around the ring. Do this for a few minutes until the putty becomes visibly softer and slightly glossy. This heat application breaks down the linseed oil in the putty, making it pliable again.

While the putty is still warm and soft from the heat, immediately resume scraping with your plastic putty knife. It should now come off much more easily in larger, gummy pieces. For any extremely stubborn, thin layers, you may carefully use the edge of a utility knife blade. Hold the blade at a very low angle (almost flat) against the porcelain and use a shaving motion to lift the residue. Reheat the putty as needed if it begins to harden again.

After scraping, a thin, oily film or residue will likely remain. To remove this, apply a small amount of a suitable solvent to a clean cloth. Mineral spirits are highly effective. Alternatively, rubbing alcohol or a commercial adhesive remover like Goo Gone can be used. Gently rub the residue in a circular motion until it dissolves and lifts from the surface. Remember to test the solvent on a hidden spot first.

The final step is to thoroughly clean the surface to ensure it is completely free of any oils or residues, which is critical for a good seal with the new putty or sealant. Use a degreasing cleaner or denatured alcohol on a fresh, clean cloth or paper towel. Wipe down the entire area where the putty was located. Run your finger over the surface; it should feel perfectly smooth and clean ('squeaky clean'). This ensures the new fixture will seal properly without leaks.