ward off, evade, parry, block
搪 centers on defensive hand actions: warding off, evading, parrying, or blocking an incoming threat.
搪 combines the hand radical 扌 with 唐, which likely contributes the sound. The exact historical development is uncertain, but the structure suggests a phono-semantic compound where the hand radical indicates a manual action.
The hand radical 扌 beside 唐 suggests using your hand to ward off or block something. Picture a hand pushing away an incoming blow.
For トウ, imagine using your hand to parry a toe (トウ) that is trying to kick you: toe -> トウ, and your hand blocks it.