Consideration
Compassion, Sympathy
noun
If you dispatch what you think to the other person, you're thinking about them, and you're being nice. You're showing consideration, sympathy, and compassion for the other person.
One reading comes from 思う, so that's all good. 遣り has a weird alternate reading, though (やり). To remember it, just think about how much consideration you're always showing. You're always like "Yah (や), yah, no, I totally understand. SOOO sad." /end sympathy/
思い遣りのつもりだったのかもしれないけど、嘘なんてついてほしくなかった。
Maybe you did it out of consideration, but I didn't want you to lie.
思い遣りのカケラもない奴だと思っていたが、そんなことはなかった。
I had thought he was a man without a shred of compassion, but I was wrong.
こんなに臭い部屋でいつまでも待たせるなんて、あいつはなんて思い遣りのないやつなんだ。
It’s not very considerate of him to keep us waiting for so long in such a stinky room like this.