A better question is where did Eirin learn to spell it?
Well, you know, granddaughter of the Brain of the Moon and all that.
She actually just writes it phonetically; as long as she knows her hiragana, she can "spell" it correctly. Since it's written correctly in hiragana, misspelling it in English wouldn't be accurate. If you need to justify it in translated context, imagine that she's already learned how to spell "itch" or "ditch" and just worked it out from that. :-)
Updated
Bitch
Here!
So, let's see yours, Hime!And don't you ever use that word again!!We are not giving it a name like that!Aw, what's wrong with "Bitch"?You don't need to know that!The movie series Mama was watching was The REISEN directed by Nise Golgo. The fact that the lead actress resembles Mama is big topic in her head.Hey, what's "Bitch" mean, huh?That's right...I was watching that...!
Ggh...
They were saying on the TV you were watching at night, Mama.