She's a Phoenix, not a Crane (or a Scorpion, for that matter), so I don't think the point of a test would be to trap us but more to find out if we're trustworthy or not.
While we've only known Mariko for a handful of days, we've barely talked with Asako Tani. If we don't flirt back right now, we're sending the signal that we actually cared about Mariko, which I don't think is a bad signal to send (if we do flirt with her, I'm afraid we're gonna be sending the opposite signal, which is that we seduced Mariko in order to manipulate her, which doesn't improve our trustworthyness at all). Asako Tani also hasn't acted especially proud/easily angered until now, so I doubt she's going to be angry at us for not flirting back unless me massively blow our etiquette check.
Edit:
Should be going to bed, though, so I won't be able to reply to any replies to this until tomorrow.