You've taken a decision from someone. By doing this, you've created a kind of arrangement with them. Imagine yourself pulling this decision out of the person. They don't want to necessarily give it to you, but they're letting you pull it out of them, kind of. When you've pulled it out, you've come to an arrangement, though they've pulled some of your decision out too.
This word uses the kun'yomi reading for both kanji, which you might have guessed already since there's hiragana sticking out of both of them. The 取り comes from 取る and the 決め comes from 決める. Put them together and what have you got? Bibbidi bobbidi とりきめ!
I'm worried about whether they'll obey the agreement.
You should make living arrangements with your roommate.
According to the contract between our company and Ms. Salmon, it is unfortunate, but we did not make an agreement regarding her appearance in our competitor’s commercials.