After the King had that small talk with Rei, he remembered he has something else to do in his room, and so, Rei decided that she will accompany him back to his room as she is concerned about his health despite the King insisting that he is alright.
While walking on that usual narrow path, Rei feels that she had caught more attention than before, well, she is walking with the King of that kingdom after all. However, that's not her concern at all, what she was concerned about was that, there wasn't any servants or maids that were following them although he is the ruler of a Kingdom, it's just two of them. And as she recalled when he sent her back to her room earlier, there weren't any servants that are following them either.