This is the 13432nd most frequent Korean word.
떼니
"떼니" is a conjugated form of the verb "떼다," meaning "to remove" or "to detach," used in a conditional sense like "if (I/you/etc.) remove/detach."
떼니 is used to indicate the reason for an action or state, meaning 'when separated.'
그는 나를 떼니 아무렇지도 않았다.
When he separated from me, I wasn't affected.
떼니 is used to describe the action of taking something apart.
책을 떼니 이해가 되기 시작했다.
When I took the book apart, I started to understand.
떼니 here means 'when removed,' describing the consequence of removing the picture.