Oner said she borrowed power. But as you just said she does not 'borrow' but 'takes'. She's like that Arrancar Byakuya fought in Bleach. The Arrancar took control of limbs by looking at them or the entire body by looking at the head. Satoko does this in a method similar to chakra strings that puppeteer ninjas in Naruto. In a similar string to the ninjas she can also boost ones mobility and strength through her strings.

Also by looking down on and, for the most part, insulting her powers you insulted her since her power is a literal extention of herself.

Also about relaxing Letter, that's something you have to do yourself.