“Then Jephthah sent messengers.” Why Jephthah sent messengers is unclear. It may have to do with dignity and propriety, and perhaps also not wanting to be personally confrontational. It also keeps Jephthah safe from harm.
“What is there between me and you.” An idiom. The idiom has a wide range of meanings, and so the context sets the meaning, but in this case that is difficult. Jephthah could have been trying to make peace, saying, “What is the reason you are doing this,” or it may be more aggressive, “Why is there a fight between us?” It might be like our English, “What’s the problem here?” The idiom is used in 1 Kings 17:18; 2 Kings 3:13; 2 Chron. 35:21).