Is it palmed off or pawned off? Surprise! Both are correct and mean basically the same thing: to offload something. There are subtle differences: palmed off is the trickier way to get rid of something and pawned off is more business-like.
The expression palmed off has a sneakier vibe than the other one. This use of the word palm has roots in your hands (gross), but not in chess. A shoplifter might quickly palm a necklace and put it in her pocket. Or a card sharp might hide an ace in her palm. If you palm something off, you're getting rid of it underhandedly. Here are some examples:
The other cards are similarly dealt with, and the prepared ones are finally palmed off, disposed of, and the pack again passed for inspection. (Herbert de Caston)
Many compositions by other composers were palmed off as works by Pergolesi, including several that Stravinsky incorporated in his ballet "Pulcinella" thinking they were authentic. (New York Times)
When you pawn something, you sell it to a pawn shop with the understanding that you can buy it back by a certain time. If you pawn something off, you’re getting rid of it, maybe for money. Often, the phrase is used interchangeably with the other one, but these examples bring out the pawn in pawned off:
Hunger began to gnaw at their bellies, and they pawned off their gold. (Washington Post)
The laptop and golf cart were eventually reclaimed, but the remaining items were pawned off for quick cash, a fraction of what they were worth. (Washington Times)
Rumor has it that palmed off was first and pawned off came along because they sound the same, but the expressions are used interchangeably and have been for years. If you want to be nit-picky, use palmed off when it’s straight up sneaky and pawned off when there’s money involved.