The Lunar Veil (月の羽衣 Tsuki no hagoromo) is a piece of Lunarian technology which allows the wearer to fly, even between the Earth and the Moon, but also causes them to lose their spirit - after using one Reisen mentions that she has few memories of her journey (and when she visits Earth again via Toyohime's power, it doesn't seem to be familiar to her). Described as the most primitive and time-consuming way of travelling between the Earth and Moon, the veil is used mainly by moon rabbits. However, Kaguya Houraisan was intended to be returned to the capital via a lunar veil so that she would forget her attachments to Earth.
The veil resembles a piece of silvery cloth; it has zero mass, being spun from moonlight, and Eirin Yagokoro can easily recognise the wavelength of its shimmering light from a distance. Eirin mentions that the veil is frequently confused for the antimatter robes of a celestial maiden, but that they are completely unrelated.
Reisen used a lunar veil to travel to and from the Earth in the events of Touhou Bougetsushou. Reisen Udongein Inaba also used a veil to flee to Earth in the backstory - this veil was kept sealed at Eientei until Silent Sinner in Blue chapter 8, where Eirin secretly attached part of it to Remilia Scarlet's Moon Rocket to act as a beacon.