Great idea, if you can do it without scratching or marring the glaze on the tile. The best technique to use will depend on what type of paint it is. Do you know if it's latex or oil? It's likely to be oil paint because it's in the shower area, but it would be good to know for sure because you could use a gentler process if it's latex. Since it's an old house, it's possible that it's lead paint (if it's an oil-based paint -- latex paints didn't contain lead AFAIK). Also, be aware that the PO may have painted the tile because some of it was damaged.

One way to test whether it's a latex paint is to wet a rag with denatured alcohol and rub an inconspicuous spot. If the denatured alcohol softens the paint or if the paint comes off on the rag, it's latex. (Obviously, use a dark rag since the paint is white.)

If it's latex, the paint should be relatively easy to remove, at least from the tile. (Removing the paint from the grout may be tougher.) I would first try to soften it with a heat gun (testing first in an inconspicuous spot) and gently rub it off or carefully scrape it off with a razor blade or putty knife. If that doesn't work, try a latex remover such as Goof-Off before resorting to a chemical stripper, which could damage the glaze or the grout. If you do have to use a paint stripper, you should be able to use a relatively mild one to remove latex paint. (IME, just about any paint stripper works well with latex paint -- not so with oil paint.)

If it's an oil-based paint, you'll probably have to use a stronger paint stripper. Look for a paste-type stripper that will cling to the walls. Before using, it'd be smart to call the paint stripper manufacturer and ask if the product is safe for tile and grout. Use good ventilation and be careful not to let the stripper come in contact with any vinyl, fiberglass, or cultured marble surfaces. If the stripper damages the grout, you may have to re-grout.

Let us know what works.

Thanks so much dilettante! That is super helpful advice. I will dig out my rags once my DH leaves for work (he is against this project :-) Thanks again -

I would love to see pix! I would also want to save the vintage tile, so completely understand ;)

You can definitely remove the paint, and your GC is wrong. It doesn't have to scratch the tile.

Get the thick-bodied remover that you paint on and peel off - there is some that even comes with a cloth to help peel off the paint (like waxing your legs)

If you have the marvelous deep teal/jade tiles, I envy you!

I just removed paint from pink tile in a 1955 bathroom. I used Jasco Premium paint stripper and both a plastic and metal putty knife. The stripper worked well to wrinkle both coats of paint (primer and topcoat) and I could strip large sections holding the knife at a 45-20 degree angle. It's still a lot of work. My metal putty knife has a curved corner and allowd me to scrape out the painted grout. I used acetone to complete cleaning the remaining grout and paint. No scratches on the tile are evident. It CAN be done, it just takes time and patience. Always test an area of tile first. I saw that the metal putty knife did not scratch the tile, otherwise, I would have continued with the plastic putty knife. The metal knife speeds up the process.