I just re-read the last handful of chapters of Book 0 in light of what's happening here in Chapter 23. Regina did get awfully attached to Maytag, and even after she hooked up with Lucient, she was much more affectionate toward May. She worried about her openly, and that clearly bothered Lucient. Perhaps Regina's feelings for Maytag were what drove her and Lucient apart.
One thing struck me about May and Regina's night on the town. I remember Regina used to hurt herself to get Lucient's attention... well, when May was busy listening to the amorous couple in the booth next to theirs, Regina appeared to pass out drunk. May looks at the bottle and is like, when did you drink all that?! I wonder if Regina wasn't just putting on an act so that Maytag would take care of her? So she could be close to her?
Moss has said that Maytag's weakness is her promiscuity. I wonder now if Regina knows that May is with Bern (or even if she cares). It's unclear if she actually saw what happened in the tub or if was just told about it. But it seems to me that Regina's feelings are genuine... this could be a test for Maytag on many levels, not just the one Danzig and co. might have in store for her.