I just got trespass banned from Paris in Las Vegas (owned by Caesars). They said I would get arrested if I walked into any properties owned by Caesars. Does this extend to properties that are only leased/operated, but not owned, by Caesars?

This is the first time I've gotten trespass banned, so any other information regarding getting banned would be helpful. Have you gone back to a place you were banned from? What happened?

EDIT: Also, I had a Caesars rewards card. Is it a bad idea to let someone else go in a use any points on it? Will they wipe my rewards?