I've driven many rental cals across the border, both US cars into Canada and Canadian cars into the US. I've never once told the rental agency that I was doing this trip, never once had any issues. A few times I was asked by the agents if the vehicle I was driving was my own, and I responded "no, it's a rental" and that was the extent of it -- never had a contract verified or anything like that. I don't think you'll have any issues.