Yes, you only keep them if you restart from the checkpoint.
It was written somewhere in a card (probably on the ones that explain the "checkpoint system", but I don't remember)
We didn't read that rule as a misprint and did the opposite.
From what I can tell, every item in the second part of the game has that logo. (Except maybe the map?).
The point being, the checkpoint introduces a new rule: you can reset to that point, using the stats/tokens you recorded on the time log, and keeping all items in your possession. Note that you don't record items on the time log. You just keep everything in your hand.
The new icon then overrides that new rule: these items must be returned when you restart. So essentially: you keep the items you had at the checkpoint, you lose any you got since. But there's not technically any way to know which is which, that symbol is there to let you know what items come from the second part of the game and must be returned.