Grigor's note says, "The letters around the empty squares indicate which letters belong in what row or column. If I place all the letters into the squares in a continuous line alphabetically, that should unlock the box." Yeah, that's helpful.
Grigor also says Xenia keeps her notes in that box, so we need to get into it. Read to the end of this hint showing how to solve this puzzle.
To translate Grigor's note into English, this is an alphabet version of the renogram puzzles in ND 23, Shadow at the Water's Edge. That is, you're inserting the alphabet into this grid in order, from A to X. To put a letter in a square, click on the square, then click on the letter at the left. The highlighted letters are those that haven't been placed yet.
There's the added help (or maybe it's a hindrance) that the letters around the outside of the box indicate that those letters are in the row or column they're next to, but you don't know where.
And not all the letters are included. The A is put in place, thank you, but B could be anywhere. The only help is that you know which row or column C is in, so the B has to be somewhere that allows it to reach the C spot from there.
This is a puzzle that generally requires a lot of backtracking. You put in a half-dozen letters, then discover that you can't reach G from where you put F, so you then have to undo all the letters you just did and start over. Ngh!
The more letters you put in, the easier it gets. You might consider looking at the picture below just enough to find a couple of letters, or just the letters in the first column, and then try to do the rest of the puzzle yourself.
In any case, here's the final arrangement of letters you need: