Thanks for the chapter!
Manga left it out but in LN after Consort Yun chastised Consort Bu she announced that she had thought of attending but is now too afraid to and left. This enraged the Emperor so much he started beating Consort Bu severely. Her father, Secretariat Bu tried to plead for his daughter's life resulting in the Emperor hurling Consort Bu into her father resulting in his death and her being severely injured.
As for the Bu family's invitation it's likely that due to not being able to blame or hold the Emperor responsible for Secretariat Bu's death, they've decided to blame MC for angering Consort Bu by beating their daughter in a competition. Essentially blaming for everything rather than holding any of their family responsible for not keeping their temper. So some form of insult or shenanigans are likely to ensue once she arrives based on grandma's reaction to invitation letter.