scratcher
揥 is a rare kanji whose core meaning is a scratcher, a tool for scratching. Its standalone meaning is narrow and specific.
揥 combines 扌 (hand) with 帝, which likely provides the sound. The exact historical development is uncertain due to the kanji's rarity.
The hand radical 扌 beside 帝 suggests a hand-held tool. Imagine an emperor (帝) using a hand-held scratcher to relieve an itch.
For テイ, picture a tailor (テイ) using a small hand tool to scratch a mark on fabric: tailor -> テイ, and the hand 扌 holds the scratcher.