Then he had come to the tabloids of the excellent M. Najdol. These guarantee, on the label, ‘Refreshing and absolutely natural sleep to the soul-weary.’ They are carried in a case with a spring which presses one scented tabloid to the end of the tube, whence it can be lipped off in stroking the moustache or adjusting the veil.
This is from "In the Same Boat " by Rudyard Kipling.
https://www.kiplingsociety.co.uk/tale/in-the-same-boat.htm
I don't understand the meaning of whence it can be lipped off in stroking the moustache or adjusting the veil.