Yes, the fl and crown prince get into a physical argument involving it.
I'm letting this marinate a bit so I don't know if this next part is a spoiler or if it's even included in the manhwa. So (potential) spoilers ahead.
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CP realizes FL has feeling for Varkis and they get into it because she says that she also knows something that he doesn't want people to know. Which is the rumor about who was the first woman he slept with and what sort of appearance he looks for in women. After that (if I remember correctly) he starts choking her.
Oh dear, he deserves to rot !!!
I know it showed the step mother but was it already confirmed in the novel the Crown Prince lusts after the step mother ?? Cause the FL looks exactly like her unless her hair color is described differently in the novel