The most important promise or understanding that exists between Dill and Scout is the fact that they are committed to be engaged to one another. Dill sort of proposes early in the book with the innocence of a child and it is understood from that point on that they will be together eventually even though at this point, they do not even understand love.
Throughout the text, a few interestingly ironic events happen that promote this idea. In chapter 14, the two children lie in bed together talking about where babies come from. At this point, they are likely both too young to know where they come from. Scout also has many moments throughout the text as a whole where she thinks fondly of him and misses him like a child misses a friend. Their relationship grows throughout the text as they age and Jem is interested in increasingly mature things.
Although Dill and Scout claim to be engaged (Perhaps this is the understanding you ask about?), they also have other unspoken promises and understandings. For one, they never talk about Dill’s real family. Dill is constantly making references to elaborate adventures with his father. Jem and Scout both know that he is lying, but they do not dwell on it. Instead, they sometimes play along and sometimes ignore it. Dill’s family situation is the proverbial white elephant in the relationship. It is understood but never mentioned. This is one example of the respect and friendship that they share.