The phrase "a note demanding that" is correct and usable in written English.
It can be used when referring to a written communication that requests or insists on a specific action or response.
Example: "She received a note demanding that the repairs be completed by the end of the week."
Alternatives: "a message requesting that" or "a letter insisting that".
On Tuesday afternoon, Jimmy Lee Dykes, to whom Mr. Poland had given a gift of yard eggs and homemade jam days earlier, boarded Mr. Poland's bus and handed him a note demanding that he hand over two young children.
Afterward, Apple Dumplin' gives him a note demanding that he surrender and do good deeds; he reluctantly does so, giving the toddler and berries back to Strawberry and company.
Outraged, French bank Calyon, owner of $966 million of the CDO's most secure notes, demanded that payment on its principal begin and distributions to Magnetar come to an end.
Hoste was furious at the behaviour of Flore's officers and sent a note into Lesina demanding that they give up the ship as indicated by its earlier surrender.
The ballsy diva who abruptly breaks down sobbing in the finals of The Bachelor would never survive a typical comedy notes call demanding that we see hints of this frailty 20 pages earlier.
In a more bizarre case Michael received an anonymous ransom note in 1987, demanding that he pay $2 million and diamonds or threatened lacing Strauss' products with poison.
China's Foreign Ministry has sent a note to all foreign embassies demanding that such intruders not be given refuge but be turned over to the police.
Today, China's Foreign Ministry sent a note to all foreign embassies demanding that such people be turned over to the Chinese police.
MoveOn issued a press release noting the discrepancy and demanding that Facebook implement the original plan.
But Ford, he noted, also demands that suppliers meet extensive technical specifications.
