OK I just collected all puzzle pieces/letters and I can confirm that the owl mask does indeed make the purple pieces pop out more, as in they're bigger and more prominent, and slightly rotate a bit.
The puzzle solution is I WAS BORN IN THE USA which will be the password for the 19th chapter, which you can enter on the computer before the sewer manhole
It'll be revealed as you go down and talk to the 2 cleaners that they're actually Nationalists doing secret work to manipulate people into breaking the Ruso-American coalition, and they work for a bigger foundation and stuff. The 2 themselves did volunteer and plan the whole phone thing by themselves but it's still all part of something bigger from the foundation, which motorcycle guy is apparently a member of too as well, at least from what I understand
Here's a video for those who can't be bothered finding them all, heavy spoilers of course so just click if you're really that lazy
dunno why it looks super retro VHS artifact-y on YouTube, the raw FRAPS looks cleaner but eh w/e it still looks cool lol