Does it matter if I activate mementos in the ideal number of moves?

Throughout the game, you're asked to complete various memento puzzles. The game keeps track of the amount of moves it takes you to complete a single puzzle and shows an Ideal score.

It apparently even keeps track of the total moves that you've used throughout the game to complete the puzzles in the Overall score.

Does this number have any effect on the game's story or ending? Are there achievements associated with it? Does it do... well, anything?

Solution 1:

I beat all the puzzles in the ideal number of moves in my first playthrough, and spammed my way through the puzzles in my second. I didn't notice any difference at all, unfortunately.

[Edit] Apparently the developer is still playing with adding achievements, so perhaps there will be an achievement for this in the future. However, when asked about this, the developers' official response was:

¯\_(ツ)_/¯