In certain ketubot I've seen the home of the kallah is referred to as Beit nashe, meaning the house of forgetting. What is the reason for referring to the kallah's home that way?
I think you mean nasha or nashei as is the k'suba formulation (see Rashi on Bava M'tzi'a' 104b, s.v. מקום שנהגו לעשות):
ודין נדוניא דהנעלת ליה מבי נשא
The expression מבי נשא essentially means "from the house of her father".1 See Tosafos (Shabbos 23b, s.v. דבי נשא דרב שיזבי), who cites a dispute among rishonim regarding whether this phrasing should only be used in a k'suba if the bride's father was already deceased, since there are apparent instances of this term in the Talmud where the father was still alive.2
In any case, some rishonim prefer the phrasing "מבי נשא" where the bride's father is deceased, as "מבי אבוה" might be read to imply specifically that the father is alive (e.g. ספר האגודה, Eruvin 15b).
I'm not certain of the etymology, but it might literally mean "the house of women" (since the father is deceased), or "the house of forgetting" (as a reference to forgetting the mourning of the father), or "the house of upbringing" (since it is where the child was raised).
2 For example, Shabbos 156a, "לוי בריה דרב הונא בר חייא אשכחיה לגבלא דבי נשיה דקא גביל וספי ליה לתוריה בטש ביה אתא אבוה...".