The requirement to have parental consent has exactly nothing to do with immigration law. You will find it nowhere in Title 8 of the United States Code (see chapter 12) nor, I think, in Title 8 of the Code of Federal Regulations (see chapter I, subchapter B).
Therefore, a child's immigration status does not affect this requirement, nor does the status of the accompanying adult. Even US a citizen child traveling in the company of a US citizen adult should have a parental consent letter. The point of this letter is to serve as evidence if the immigration officer suspects that the child is being abducted. If an immigration officer suspects as much, it is the officer's duty to investigate.
On the other hand, this is not actually a requirement. It is a recommendation. The CBP page linked in the question says this explicitly:
U.S. Customs and Border Protection (CBP) strongly recommends that unless the child is accompanied by both parents, the adult have a note from the child's other parent (or, in the case of a child traveling with grandparents, uncles or aunts, sisters or brothers, friends, or in groups*, a note signed by both parents) stating "I acknowledge that my wife/husband/etc. is traveling out of the country with my son/daughter/group. He/She/They has/have my permission."
Note the words "strongly recommends." Note also a subsequent sentence on the page:
While CBP may not ask to see this documentation, if we do ask, and you do not have it, you may be detained until the circumstances of the child traveling without both parents can be fully assessed.
If they "may not ask to see" the letter, then it is surely not strictly required. Later still on the same page:
Adults traveling with children should also be aware that, while the U.S. does not require this documentation, other countries may have a requirement and failure to produce notarized permission letters and/or birth certificates could result in travelers being refused entry (Canada has very strict requirements in this regard).
That this letter is not required also applies regardless of the citizenship or immigration status of the child and the adult. Foreign children arriving with foreign adults do not necessarily have to show a notarized letter, and if your child travels with grandparents without such a letter, it's quite possible that there would be no problem.
The burden of providing such a letter is small, however, and the inconvenience of being asked to prove permission without a letter could be very great, so it's probably wise to provide the letter.