I don't actually know who Alyssa is. I'll probably have to reread the comic to establish that.
I'm kind of curious why it's a bad time - hopefully that's not something which will be worstened by Claw's presence.
In NG+, Alyssa is an old friend of Grain's that he met after being taken in by Zachary. She is seen here (http://dhscomix.com/pcomics/pcomic.php?p=135) and here (http://dhscomix.com/pcomics/pcomic.php?p=136). We're only being formally introduced to her now, though.
Alyssa is also a recycled character from the original New Game, where she was an entirely different and rather creepy person (as (http://dhscomix.com/ncomics/ncomic.php?p=46) seen (http://dhscomix.com/ncomics/ncomic.php?p=176) here (http://dhscomix.com/ncomics/ncomic.php?p=74).)