If you look at the whole sentence, you'll see that the last phrase actually explains the phrase which you're asking about. The verb 'tweak' means to make a slight adjustment. tweaking the way we channel our thoughts = modifying our perception of things The explanation is already there in the sentence.

In that sentence, the phrase "tweaking the way" means that the person is changing how he or she thinks about the topic and possibly looking at an idea in another way. This can be seen as you learn about another culture. The more you learn about the culture the more you begin to see how they view things differently and this can either lead you to change your view or respect how the people of the culture view it.