Pretty cool ! I can see you're Obra Dinn fans because you not only made a similar deduction game, but also used a similar dithering shader ;) -- careful though, it got in the way of readability of small words e.g. on the diner's menu.
Unless there was some easter egg I missed, I'd say it'd be fine to just copy words on the clipboard rather than removing/exchanging them since modifying the documents doesn't seem to have any effect. (That said, I would also absolutely love if the core mechanic was to modify documents by swapping words until some conditions are met. It sounds like a hard mechanic to design around though, you may want to put some limits on which words can be moved).
Honestly, although you claim what's strange is the character's job vs. what they'd want to do, I found the diner to be pretty strange itself !
Anyway, it was fun !