I thought Arnav spilling the tea bore some symbolism to Arshi's relationship status. Here's what I think.
Mami was explaining to Buaji and Garima that while she was well aware of the differences in their social status, it was all 'love ka chakkar'. Just then Khushi comes up to Arnav to hand over the tea and Arshi's eyes meet. He is in a hurry to sip the tea but the cup slips and stains his white shirt.
Here the tea could signify Khushi's considerate, caring, bold and sometimes crazy nature which attracted Arnav to her. The cup slipping could be symbolic of Arnav' s missed kiss when in the hurry to express himself he forgot himself for a moment and was about to give in to his feelings. The stain on his white shirt seemed to be symbolic of his engagement announcement to La which was a knee jerk reaction to his missed kiss.
Arnav goes into the kitchen and asks Khushi for a napkin. (Must say that this guy knows how to make himself at home in her house. The first time he came carrying her unconscious in his arms, he walked straight into her bedroom and yesterday he walked into her kitchen.)
Arnav tried to remedy the situation to some extent when he tried to get her to reveal her true feelings about his announcement so that he too can open up to her.
Instead of giving him the napkin, Khushi tries to wipe away the stain and ends up making it more messy.
Khushi tried to put up a brave front and pretended that she was happy about his announcement and she herself got engaged to Shyam (although it was under coercion). The blot in their pure relationship (the white shirt) became bigger.
Khushi volunteers to clean up the mess but Arnav says he will do it himself and asks her the way to the bathroom. She shows him the way and he returns after cleaning his sleeve.
While Khushi will try to do her best to undo the damage done to their relationship (the first step being breaking off with Shyam after she finds out the truth), Arnav will be the one who will be in a position to return their relationship back to its pure status. In this he needs to be guided by Khushi for he does not know the way.