It's been literal years since I read the novel (I looked it up when this manga was first posted, four years ago), so I honestly don't remember. ( ̄∇ ̄")
Guess I'll go reread the novel and get back to you. Gimme a minute...okay.
You will probably find out where those rumors came from...basically immediately when the next chapter is posted. The saint has nothing to do with it (as I expected). She's just a normal girl!
It was actually Katrina who did it. She started spreading those rumors because she used to be a fiancée candidate for the prince, and she's super jealous that Rachel got chosen instead. One of her friends has strong magic and can see spirits, so she told Katrina about the cat, and Katrina knows through her father that the prince has been researching for the past while. So she did the math and is trying to get Rachel dropped so she can take her place. (〜 ̄△ ̄)〜
This entire drama is wrapped up in like three chapters. The family almost had their noble status revoked over this; instead, the father has to step down and give his son his position as head, and the royal family will be observing them (their next mistake will probably cost their house). And Katrina is sent to a convent.

That saintess gonna be another annoyance why can't main characters and the villainess be friends like seriously, where is the "girls for girls" agenda, the camaraderie through thick and thin