'민하님이 따주셨음.' => 민하 picked (it) for me. (most likely meaning)
It is hard to say for certain because 따다 has multiple meanings: 1) to pick/pluck (fruit, flower, etc), 2) win money in a game or gambling.
- 따주셨음 = 따다 + -아/어 주시었다 + -(으)ㅁ -> 따(서) 주시었음 -> 따 주셨음.
- X-아/어 주다 = do X for someone. e.g. (동생의) 숙제을 해 주다 = do the homework for (my brother).
- 주시었다 = 주시다 (honorific form of 주다) + -었다 (past tense) => did for (me).
- -(으)ㅁ = special ending for succinct, impersonal effect (used on Internet and in personal notes).