"The Overbearing Grandpa Yofan"

Why would these people kill Ainsley once they knew she's the one bringing Code-C out of the prairie?

Because the ownership of the sacred guardian can't be transferred until the one summoning them out is dead or they give their consent to transfer the ownership.

Even if the sacred guardian is still in a cat form and doesn't transform yet, the ownership imprint is still there until the day the owner releases the imprint to return the beast to the prairie. It happens when the owner can't handle the beast anymore.

But if these sly old men knew that Ainsley was the one holding the ownership imprint, couldn't they just kill her in silence to grab the ownership?

Owning a sacred guardian was akin to establish one's foothold in the Sloan Family! Even other mafia families would have to be wary against this person who tamed the sacred guardian.