Unless people are being vaccinated on the forehead or right hand, they're doing it all wrong for the 'mark'. The Bible is very specific -
Rev 13:16 He also forced everyone, small and great, rich and poor, free and slave, to receive a mark on his right hand or on his forehead, 17 so that no one could buy or sell unless he had the mark, which is the name of the beast or the number of his name.
There are events which precede the mark that haven't happened yet, such as -
Rev 13:13 And he performed great and miraculous signs, even causing fire to come down from heaven to earth in full view of men. 14 Because of the signs he was given power to do on behalf of the first beast, he deceived the inhabitants of the earth. He ordered them to set up an image in honor of the beast who was wounded by the sword and yet lived. 15 He was given power to give breath to the image of the first beast, so that it could speak and cause all who refused to worship the image to be killed.
So again, the Bible shows us the vaccine is not the mark. I'm not saying the vaccine isn't complete crap and potentially serving a hidden agenda, but there's no need to add fuel to the fire and mislead by claiming the vaccine is the Biblical mark of the beast when it's not.