Thanks to Noe's efforts (and some hard work from Koume, to be fair) Ouka-kai are now kitted out with plenty of information about their future opponents at Asaka school, and not a moment too soon, as they finally record a win (and comprehensively so) in one of their practice games. The trouble is, Koume has left a photograph from said notes floating around, which leads to problems and misunderstandings aplenty this episode.
In short, Koum's parents assume that the photo they find of Takahara means that Koume is dating (or at least intending to date) him, and so we enter a row between Koume and her parents based entirely upon misunderstandings... a state of affairs which ends up spreading to Saburou, as the whole thing gets completely out of hand.
Meanwhile, following their improvements and practice victory, Ouka-kai send off an official challenge to Asaka - One which is summarily rejected by the head of the school against the wishes of the baseball team there. It takes some people in high places applying pressure to change the head's mind, so the game is now on, leaving the girls needing the summer break to train and improve further still.
I'm really not quite sure how this series does it, but Taishou Yakyuu Musume has somehow just about managed it again - Taking a horribly cliched and over-used concept (the old talking about different things and misunderstanding one another deal), yet actually making it quite fun to watch both by making the entire state of affairs rather adorable and also giving us characters (Koume in particular) who you can't help but want to get behind and cheer on. Yes, this might well have been the least inventive anime plot of the current season so far, but I suppose it shows that even tired old ideas can work okay if you weave them into the right story with the right characters.