I think the problem would not be exactly Tremolo fucking HOTs for money (although I don´t think Sage would be OK with that), but Tremolo knowing first hand (not only having suspicions) about Quinn using the HOTs as a coverture for her dirty business, and not telling her.
Sage is the president of the HOTs, and, if there is some kind of scandal related with the HOTs, she´s going to be responsible of that, even if she was in the dark about it. Something that Sage hates, we already know, is dishonesty. One of the main things that make Sage be fond of Tremolo is that Tremolo always sticks her side and doesn´t lie or hide things from her. If Tremolo was maintaining Sage blind about the things that are happening inside her own fraternity because he was involved in it (even if just as a client), I think is going to be a deal breaker for Sage.