Tegaki refers to posts made by Ohtaka on her blog, which used to be on tegaki.pipa.jp. Nowadays, it's on Wordpress, but the posts are still typically called tegakis. So these are posts that were made by the mangaka herself, but were not officially published.
Aladdin's first-person problem:
In this tegaki, Judar makes fun of Aladdin for mixing up boku and ore in his speech. Hakuryuu, who used to have the same issue, punches Judar right through his borg out of embarrassment, albeit without intending to. However, later Ohtaka added an additional panel, in which Judar is outraged, saying that not even the Al-Thamen guys ever hit him. Hakuryuu hurries to him, asking if he's okay, clearly not having intended to punch. Aladdin asks Judar how come his borg seems to malfunction on Hakuryuu.