From the moment that Mitch and Blanche are introduced, it is clear to the audience that they have a 'certain interest' in one another. Immediately previous to their meeting, Mitch talks of his 'sick mother'. This reveals a sensitive side to his character, which contrasts with the vulgarity and coarseness of his peers. Blanche has clearly been unimpressed by the manners of Stanley and his other friends, which hints that she will like Mitch rather better.
Mitch leaves the room just before Blanche enters. Their rather unexpected meeting at the bathroom door draws attention to their introduction. Mitch speaks to Blanche with 'awkward courtesy'. Unlike his contemporaries, he seems to recognise how an upper class woman should be treated. He clearly does not use these manners in every day life as perhaps Blanche would, but the effort he makes on her behalf is significant. As Mitch excuses himself there is a rather awkward incident where he forgets to put the towel back.
It is her flirtatious manner that provokes this absent-mindedness. His subsequent 'embarrassed laugh' reflects his fury with himself for making such a blunder, and reveals how much he desires her good opinion.
For Blanche's part the audience has already been introduced to her rather flirtatious nature. Before she enters the room where the men are playing cards, she asks how she looks. She has already expressed her disapproval of Stella's marital choice on the grounds of Stanley's class. The audience can therefore reasonably conclude that she would not wish to make a similar choice for herself. The fact that she wants to be found attractive by a group of men with whom she would never consider forming an attachment highlights her vanity. It is therefore unsurprising that Blanche is charmed by Mitch's obvious regard for her. However...