Does anyone know how to clean an old grimy Raggety Ann cookie jar?

Use white toothpaste (not gel) and a damp toothbrush. Lightly brush and wipe off with a cloth or paper towel. I use this method on everything I sell on Ebay, except clothing. Works on jewelry, ceramics, copper, brass, even sneakers. Last year I sold a Tweety Bird cookie jar I purchased at a garage sale. It happened to be a smokers home. Toothpaste cleaned several years of nicotine off.

Try making a paste of baking soda and water. It is more gentle than Comet or some of the other cleaners that might scratch the original paint. Just go gently to make sure it doesn't clean too deep.

I think I'd try the dish washer. It sure removed the sticky feeling from reality old Tupperware

Try tea tree essential oil on a cotton ball. I have discovered that it will take off any type of greasy grime. My mom's picture frames were terrible.