I thought it was a common trope, and then I thought maybe it was just one movie, but at this point I just can't find any evidence that I saw this anywhere, but I'm looking for a character or characters in books or film that regularly steals things and justifies it as "trading" because they leave something of significantly lesser value behind after each theft. The example I seem to recall is an exchange going something like "you stole that?!?!" "No, I traded a very fine knife for it."
I've put hours into the search on sleepless nights and I wonder if you can do better.
Logan from Gilmore Girls did something similar to this: he and his friends would steal trinkets from rich people, then swap them out for trinkets from other rich houses. It's not exactly the same as your description, but it seems like the writers below have heard of this other places as well.
Dear Endlessly Frustrated,
This sounds a lot like the game Bigger or Better, where kids or teens go door-to-door and ask their neighbors to trade an item they're carrying for something bigger or better in their house (hence the name). Last time one group knocked on my family's door, we got an underripe pineapple in exchange for our checkers game. I want our checkers game back, Josh.
Wayne from The Alloy of Law by Brandon Sanderson is EXACTLY like that. He does things like leave random drawings he made in lieu of nice clocks, or taking evidence from a police locker and leaving a knife in its place. No one has to agree to his trades in order to make them, he just sort of leaves whatever he has around in order to take things he finds interesting or useful at the time.
I initially thought Tasselhoff Burrfoot from the Dragonlance books might meet your parameters. Tasselhoff is a kender, a humanoid species that--among their other traits--tend to end up with things that aren't theirs. When I asked a friend familiar with Dragonlance, however, my friend clarified that the charismatic and charming Tasselhoff and other kender don't steal, they just sort of end up with things in their possession via chance and a sort of unconscious pocketing. Since they don't steal consciously, they also don't switch any object for the one they've removed.
Regarding kenders and your question, it appears I've come up... empty handed.
P.S. You can read more about this particular character's personality and motivations on Wikipedia, if you want.
This definitely isn't the character you're looking for, but all the discussion of beings who steal things but don't really consider it stealing reminded me of Hashkat from Lloyd Alexander's The Iron Ring. Hashkat is a monkey king and lives by the creed that if something isn't nailed down then taking it isn't stealing, and if it can be pried loose, then it isn't nailed down.
Anyways, not helpful to your quest, but at least your mental store of fictional and amicable thieves has now been expanded.