I think the bite marks are a sort of forever promise between the 2 of them. When LBY's aunt passed away, LBY was at his darkest because he felt that he was the one truly alone now. CSS was the only light to him and he was desperate to get connected to her. The bite marks were his whimsical idea at that moment, like the blood oath between 2 lovers.
In the novel, during the years of exile, he used to stroke the arm with the bite mark and the hand wrapped with the Shao Sheng string that CSS used on him to pull out the arrow when he missed her.
When he came back to the capital, he decided to pursue her again. He discovered that CSS's bite mark had faded a lot because she used ointment on it to make it heal faster so that the mark would fade by the time she married Yuan Shen. He was so pissed off that he pinned her down and renewed the mark. Then CSS proceeded to beat him up. On the face, no less.
This part made me laugh and want to cry at the same time. I hope they will keep some of it in the drama.
BTW, I heard with VVIP account, you can binge the remaining eps of LLTG tomorrow. Tencent's in a hurry to air Xiao Zhan new xianxia drama so they have pushed the broadcasting of LLTG faster (or so the rumours said).