Yes, TRAMPED is a Scrabble word!

Letter values in Scrabble US: T 1, R 1, A 1, M 3, P 3, E 1, D 2.

Is it a valid word?

TRAMPED is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

travel on foot, especially on a walking expedition
walk heavily and firmly, as when weary, or through mud
cross on foot
move about aimlessly or without any destination, often in search of food or employment