Breakdown of jungyohan yeonrakcheoneun memojie jeokgo jiugaedo yeope duseyo.
Questions & Answers about jungyohan yeonrakcheoneun memojie jeokgo jiugaedo yeope duseyo.
The particle 는 marks 연락처 as the topic: as for important contact information... This gives the sentence a slightly instructional or contrastive feeling, like talking about what should be done with important contact info.
If you said 연락처를, it would focus more directly on the object of write down. Both are possible in Korean, but 연락처는 sounds natural when giving advice or instructions about a topic.