My interpretation:
- Mona tried to find a client, but chickened out. Burke was there (he was either Mona's intended customer who didn't know who he was, or he saw Mona trying to find a customer, or he saw a crying student and wanted to know what was going on).
Mona is a risk to Quinn and the Restaurant because she knows, but ultimately doesn't want to participate. So she puts pressure on her, using Burke's presence to make her understand that she's screwed because the head of the college caught her trying to prostitute herself. And it works, because Mona leaves.
- As for Quinn coming out of his office and Burke denying Maya the scholarship, I explain this by the “Join HOT, get a scholarship” rumor.
He's heard the rumor, so he calls Quinn in to talk about it (his role as head of the college). Quinn started the rumor to get more dishes to serve in her restaurant. Her great plan screwed up again, and worse it draws attention to the HOTs and the Restaurant, so she has to lay low for a while and close the Restaurant.
As for Maya, granting her the scholarship is the same as making the rumor true. Hence the change of heart when she says she's a HOT member.