If grease is dripping past the cup onto the deck, stop cooking. A full tray turns the next fatty cook into a grease fire. Deep clean path: clean grease tray, degrease.
Procedure
Grill cold. Tank off or pellet unplugged.
Slide the cup/tray out over cardboard. Do not tip it on the deck.
Scrape solids into the trash. Wipe with paper. Degrease the cup.
Scrape the rail and the underside of the firebox where grease bridges into the cart.
Install a fresh liner if your model uses foil pans / Traeger liners.
Reinstall level — a cocked tray overflows one corner.