And why are they on my old (but new to me) set?
The game of Mahjong changed through the years. If people were playing by the rules established by the National Mah Jongg League, the number of Jokers changed from year to year. It might sound like a good idea to have more Jokers to play with, but what does that mean if you have an old set that had lots of Flowers (the number of Flowers changed too)* but no, or not enough, Jokers?
People had to adapt. The NMJL offered Red Stickers to cover found or purchased tiles, or extra Flowers that weren't being played with, but back in the 1950s and 1960s, lots of women wore red nail polish. And red polish really stands out, and apparently when put on Mahjong tiles, really lasts! Women often painted J on any tile they wanted to turn into a joker if they did not want to bother with getting stickers from the National Mah Jongg League, or they just covered the face of the tile with a coating of polish. Of course, this was in the years before we had beautiful stickers, some designed by CHarli who you will find on the resources page. Some industrious owners even made little decoupage creations, as you see above.
The good news is that both can come off. But you have to be careful. Some stickers peel off easily. Often they are hiding some wonderful Flower tiles that you need for your set. And nail polish remover can help get rid of that polish. It really does come off. It is a pretty sure bet your tile will look better with a beautiful sticker than that J or that old dirty sticker.
* You will often find tiles that don't even remotely look like tiles in your set. It was because a previous owner was so eager to play the game that they took tiles they found and used them for play, even though if would be very obvious they were not original to the game. People did not seem to care as much back then about other people being able to figure out what tiles they had, I guess, or else they felt there was just no other choice if they wanted to play.