Yeah, its printed on my H1B.
I think, if you apply for visa on third country, you need to give a reason why you are in that country in first place. I vaguely recall that there is a question in DS160 about this as well (permanent residences/ citizenships etc). Just take your CoPR or PR card with you as a proof.
Naah no questions.
When I was planning to make this arrangement work (living in Canada and working in US on H1b), one of my core goals was to not worry.. In the sense, am I breaking in laws or is there any "grayzone" in this.
I consulted my company's own immigration lawyer and consulted with few others as well. Everyone said the same thing, there is nothing wrong there. So, you don't have to worry at all facing the CBP folks.
There is always a risk whenever you leave the US and are coming back on H1B. But living in Canada and working in US wont increase or decrease that risk. Which is to say, if you are not allowed to enter US, the Canadian permanent residency won't be the reason for that.